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Milestones in Autonomous Driving and Intelligent Vehicles: Survey of Surveys

2022-11-24
Long Chen , Yuchen Li , Chao Huang +7 more
Interest in autonomous driving (AD) and intelligent vehicles (IVs) is growing at a rapid pace due to the convenience, safety, and economic benefits. Although a number of surveys have reviewed … Interest in autonomous driving (AD) and intelligent vehicles (IVs) is growing at a rapid pace due to the convenience, safety, and economic benefits. Although a number of surveys have reviewed research achievements in this field, they are still limited in specific tasks, lack of systematic summary and research directions in the future. Here we propose a Survey of Surveys (SoS) for total technologies of AD and IVs that reviews the history, summarizes the milestones, and provides the perspectives, ethics, and future research directions. To our knowledge, this article is the first SoS with milestones in AD and IVs, which constitutes our complete research work together with two other technical surveys. We anticipate that this article will bring novel and diverse insights to researchers and abecedarians, and serve as a bridge between past and future.
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Human-Like Decision Making for Autonomous Driving: A Noncooperative Game Theoretic Approach

2020-11-17
Peng Hang , Chen Lv , Yang Xing +2 more
Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers' traffic ecology and minimize … Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers' traffic ecology and minimize the effect of AVs and their misfit with human drivers, are issues worthy of consideration. Moreover, different passengers have different needs for AVs, thus, how to provide personalized choices for different passengers is another issue for AVs. Therefore, a human-like decision making framework is designed for AVs in this paper. Different driving styles and social interaction characteristics are formulated for AVs regarding driving safety, ride comfort and travel efficiency, which are considered in the modeling process of decision making. Then, Nash equilibrium and Stackelberg game theory are applied to the noncooperative decision making. In addition, potential field method and model predictive control (MPC) are combined to deal with the motion prediction and planning for AVs, which provides predicted motion information for the decision-making module. Finally, two typical testing scenarios of lane change, i.e., merging and overtaking, are carried out to evaluate the feasibility and effectiveness of the proposed decision-making framework considering different human-like behaviors. Testing results indicate that both the two game theoretic approaches can provide reasonable human-like decision making for AVs. Compared with the Nash equilibrium approach, under the normal driving style, the cost value of decision making using the Stackelberg game theoretic approach is reduced by over 20%.
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Decision-making in driver-automation shared control: A review and perspectives

2020-07-24
Wenshuo Wang , Xiaoxiang Na , Dongpu Cao +4 more
Shared control schemes allow a human driver to work with an automated driving agent in driver-vehicle systems while retaining the driver's abilities to control. The human driver, as an essential … Shared control schemes allow a human driver to work with an automated driving agent in driver-vehicle systems while retaining the driver's abilities to control. The human driver, as an essential agent in the driver-vehicle shared control systems, should be precisely modeled regarding their cognitive processes, control strategies, and decision-making processes. The interactive strategy design between drivers and automated driving agents brings an excellent challenge for human-centric driver assistance systems due to the inherent characteristics of humans. Many open-ended questions arise, such as what proper role of human drivers should act in a shared control scheme? How to make an intelligent decision capable of balancing the benefits of agents in shared control systems? Due to the advent of these attentions and questions, it is desirable to present a survey on the decision-making between human drivers and highly automated vehicles, to understand their architectures, human driver modeling, and interaction strategies under the driver-vehicle shared schemes. Finally, we give a further discussion on the key future challenges and opportunities. They are likely to shape new potential research directions.
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An Integrated Framework of Decision Making and Motion Planning for Autonomous Vehicles Considering Social Behaviors

2020-11-25
Peng Hang , Chen Lv , Chao Huang +3 more
This paper presents a novel integrated approach to deal with the decision making and motion planning for lane-change maneuvers of autonomous vehicle (AV) considering social behaviors of surrounding traffic occupants. … This paper presents a novel integrated approach to deal with the decision making and motion planning for lane-change maneuvers of autonomous vehicle (AV) considering social behaviors of surrounding traffic occupants. Reflected by driving styles and intentions of surrounding vehicles, the social behaviors are taken into consideration during the modelling process. Then, the Stackelberg Game theory is applied to solve the decision-making, which is formulated as a non-cooperative game problem. Besides, potential field is adopted in the motion planning model, which uses different potential functions to describe surrounding vehicles with different behaviors and road constraints. Then, Model Predictive Control (MPC) is utilized to predict the state and trajectory of the autonomous vehicle. Finally, the decision-making and motion planning is then integrated into a constrained multi-objective optimization problem. Three testing scenarios considering different social behaviors of surrounding vehicles are carried out to validate the performance of the proposed approach. Testing results show that the integrated approach is able to address different social interactions with other traffic participants, and make proper and safe decisions and planning for autonomous vehicles, demonstrating its feasibility and effectiveness.
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Multi-Modal Sensor Fusion-Based Deep Neural Network for End-to-End Autonomous Driving With Scene Understanding

2020-06-17
Zhiyu Huang , Chen Lv , Yang Xing +1 more
This study aims to improve the performance and generalization capability of end-to-end autonomous driving with scene understanding leveraging deep learning and multimodal sensor fusion techniques. The designed end-to-end deep neural … This study aims to improve the performance and generalization capability of end-to-end autonomous driving with scene understanding leveraging deep learning and multimodal sensor fusion techniques. The designed end-to-end deep neural network takes as input the visual image and associated depth information in an early fusion level and outputs the pixel-wise semantic segmentation as scene understanding and vehicle control commands concurrently. The end-to-end deep learning-based autonomous driving model is tested in high-fidelity simulated urban driving conditions and compared with the benchmark of CoRL2017 and NoCrash. The testing results show that the proposed approach is of better performance and generalization ability, achieving a 100% success rate in static navigation tasks in both training and unobserved situations, as well as better success rates in other tasks than the prior models. A further ablation study shows that the model with the removal of multimodal sensor fusion or scene understanding pales in the new environment because of the false perception. The results verify that the performance of our model is improved by the synergy of multimodal sensor fusion with scene understanding subtask, demonstrating the feasibility and effectiveness of the developed deep neural network with multimodal sensor fusion.
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Cooperative Decision Making of Connected Automated Vehicles at Multi-Lane Merging Zone: A Coalitional Game Approach

2021-04-02
Peng Hang , Chen Lv , Chao Huang +2 more
To address the safety and efficiency issues of vehicles at multi-lane merging zones, a cooperative decision-making framework is designed for connected automated vehicles (CAVs) using a coalitional game approach. Firstly, … To address the safety and efficiency issues of vehicles at multi-lane merging zones, a cooperative decision-making framework is designed for connected automated vehicles (CAVs) using a coalitional game approach. Firstly, a motion prediction module is established based on the simplified single-track vehicle model for enhancing the accuracy and reliability of the decision-making algorithm. Then, the cost function and constraints of the decision making are designed considering multiple performance indexes, i.e. the safety, comfort and efficiency. Besides, in order to realize human-like and personalized smart mobility, different driving characteristics are considered and embedded in the modeling process. Furthermore, four typical coalition models are defined for CAVS at the scenario of a multi-lane merging zone. Then, the coalitional game approach is formulated with model predictive control (MPC) to deal with decision making of CAVs at the defined scenario. Finally, testings are carried out in two cases considering different driving characteristics to evaluate the performance of the developed approach. The testing results show that the proposed coalitional game based method is able to make reasonable decisions and adapt to different driving characteristics for CAVs at the multi-lane merging zone. It guarantees the safety and efficiency of CAVs at the complex dynamic traffic condition, and simultaneously accommodates the objectives of individual vehicles, demonstrating the feasibility and effectiveness of the proposed approach.
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Decision Making of Connected Automated Vehicles at an Unsignalized Roundabout Considering Personalized Driving Behaviours

2021-04-14
Peng Hang , Chao Huang , Zhongxu Hu +2 more
To improve the safety and efficiency of the intelligent transportation system, particularly in complex urban scenarios, in this paper a game theoretic decision-making framework is designed for connected automated vehicles … To improve the safety and efficiency of the intelligent transportation system, particularly in complex urban scenarios, in this paper a game theoretic decision-making framework is designed for connected automated vehicles (CAVs) at unsignalized roundabouts considering their personalized driving behaviours. Within the decision-making framework, a motion prediction module is designed and optimized using model predictive control (MPC) to enhance the effectiveness and accuracy of the decision-making algorithm. Besides, the payoff function of decision making is defined with the consideration of vehicle safety, ride comfort and travel efficiency. Additionally, the constraints of the decision-making problem are constructed. Based on the established decision-making model, Stackelberg game and grand coalition game approaches are adopted to address the decision making of CAVs at an unsignalized roundabout. Three testing cases considering personalized driving behaviours are carried out to verify the performance of the developed decision-making algorithms. The testing results show that the proposed game theoretic decision-making framework is able to make safe and reasonable decisions for CAVs in the complex urban scenarios, validating its feasibility and effectiveness. Stackelberg game approach shows its advantage in guaranteeing personalized driving objectives of individuals, while the grand coalition game approach is advantageous regarding the efficiency improvement of the transportation system.
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Continuity of the complex Monge-Ampère operator

1996-01-01
Yang Xing
The complex Monge-Ampère operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis d d Superscript c Baseline right-parenthesis Superscript n"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> … The complex Monge-Ampère operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis d d Superscript c Baseline right-parenthesis Superscript n"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">(dd^c)^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an important tool in complex analysis. It would be interesting to find the right notion of convergence <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u Subscript j Baseline right-arrow u"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mo stretchy="false">→</mml:mo> <mml:mi>u</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">u_j\to u</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis d d Superscript c Baseline u Subscript j Baseline right-parenthesis Superscript n Baseline right-arrow left-parenthesis d d Superscript c Baseline u right-parenthesis Superscript n"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="false">→</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:mi>u</mml:mi> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">(dd^cu_j)^n\to (dd^cu)^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in the weak topology. In this paper, using the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript n minus 1"> <mml:semantics> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">C_{n-1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-capacity, we give a sufficient condition of the weak convergence <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis d d Superscript c Baseline u Subscript j Baseline right-parenthesis Superscript n Baseline right-arrow left-parenthesis d d Superscript c Baseline u right-parenthesis Superscript n"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="false">→</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:mi>u</mml:mi> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">(dd^cu_j)^n\to (dd^cu)^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We also show that our condition is quite sharp in some case.
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Interaction-Aware Trajectory Prediction of Connected Vehicles using CNN-LSTM Networks

2020-10-18
Xiaoyu Mo , Yang Xing , Chen Lv
Predicting the future trajectory of a surrounding vehicle in congested traffic is one of the necessary abilities of an autonomous vehicle. In congestion, a vehicle's future movement is the result … Predicting the future trajectory of a surrounding vehicle in congested traffic is one of the necessary abilities of an autonomous vehicle. In congestion, a vehicle's future movement is the result of its interaction with surrounding vehicles. A vehicle in congestion may have many neighbors in a relatively short distance, while only a small part of neighbors affect its future trajectory mostly. In this work, An interaction-aware method that predicts the future trajectory of an ego vehicle considering its interaction with eight surrounding vehicles is proposed. The dynamics of vehicles are encoded by LSTMs with shared weights, and the interaction is extracted with a simple CNN. The proposed model is trained and tested on trajectories extracted from the publicly accessible NGSIM US-101 dataset. Quantitative experimental results show that the proposed model outperforms previous models in root-mean-square error (RMSE). Results visualization shows that the model is able to predict future trajectory induced by lane change before the vehicle operates noticeable lateral movement to initiate lane changing.
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Milestones in Autonomous Driving and Intelligent Vehicles—Part I: Control, Computing System Design, Communication, HD Map, Testing, and Human Behaviors

2023-05-29
Long Chen , Yuchen Li , Chao Huang +7 more
Interest in autonomous driving (AD) and intelligent vehicles (IVs) is growing at a rapid pace due to the convenience, safety, and economic benefits. Although a number of surveys have reviewed … Interest in autonomous driving (AD) and intelligent vehicles (IVs) is growing at a rapid pace due to the convenience, safety, and economic benefits. Although a number of surveys have reviewed research achievements in this field, they are still limited in specific tasks and lack systematic summaries and research directions in the future. Our work is divided into three independent articles and the first part is a survey of surveys (SoS) for total technologies of AD and IVs that involves the history, summarizes the milestones, and provides the perspectives, ethics, and future research directions. This is the second part (Part I for this technical survey) to review the development of control, computing system design, communication, high-definition map (HD map), testing, and human behaviors in IVs. In addition, the third part (Part II for this technical survey) is to review the perception and planning sections. The objective of this article is to involve all the sections of AD, summarize the latest technical milestones, and guide abecedarians to quickly understand the development of AD and IVs. Combining the SoS and Part II, we anticipate that this work will bring novel and diverse insights to researchers and abecedarians, and serve as a bridge between past and future.
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Graph and Recurrent Neural Network-based Vehicle Trajectory Prediction For Highway Driving

2021-09-19
Xiaoyu Mo , Yang Xing , Chen Lv
Integrating trajectory prediction to the decision-making and planning modules of modular autonomous driving systems is expected to improve the safety and efficiency of self-driving vehicles. However, a vehicle's future trajectory … Integrating trajectory prediction to the decision-making and planning modules of modular autonomous driving systems is expected to improve the safety and efficiency of self-driving vehicles. However, a vehicle's future trajectory prediction is a challenging task since it is affected by the social interactive behaviors of neighboring vehicles, and the number of neighboring vehicles can vary in different situations. This work proposes a GNN-RNN based Encoder-Decoder network for interaction-aware trajectory prediction, where vehicles' dynamics features are extracted from their historical tracks using RNN, and the inter-vehicular interaction is represented by a directed graph and encoded using a GNN. The parallelism of GNN implies the proposed method's potential to predict multi-vehicular trajectories simultaneously. Evaluation on the dataset extracted from the NGSIM US-101 dataset shows that the proposed model is able to predict a target vehicle's trajectory in situations with a variable number of surrounding vehicles.
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ReCoG: A Deep Learning Framework with Heterogeneous Graph for Interaction-Aware Trajectory Prediction

2020-01-01
Xiaoyu Mo , Yang Xing , Chen Lv
Predicting the future trajectory of surrounding vehicles is essential for the navigation of autonomous vehicles in complex real-world driving scenarios. It is challenging as a vehicle's motion is affected by … Predicting the future trajectory of surrounding vehicles is essential for the navigation of autonomous vehicles in complex real-world driving scenarios. It is challenging as a vehicle's motion is affected by many factors, including its surrounding infrastructures and vehicles. In this work, we develop the ReCoG (Recurrent Convolutional and Graph Neural Networks), which is a general scheme that represents vehicle interactions with infrastructure information as a heterogeneous graph and applies graph neural networks (GNNs) to model the high-level interactions for trajectory prediction. Nodes in the graph contain corresponding features, where a vehicle node contains its sequential feature encoded using Recurrent Neural Network (RNN), and an infrastructure node contains spatial feature encoded using Convolutional Neural Network (CNN). Then the ReCoG predicts the future trajectory of the target vehicle by jointly considering all of the features. Experiments are conducted by using the INTERACTION dataset. Experimental results show that the proposed ReCoG outperforms other state-of-the-art methods in terms of different types of displacement error, validating the feasibility and effectiveness of the developed approach.

Deep convolutional neural network-based Bernoulli heatmap for head pose estimation

2021-01-19
Zhongxu Hu , Yang Xing , Chen Lv +2 more
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Human-in-the-Loop Deep Reinforcement Learning with Application to Autonomous Driving

2021-01-01
Jingda Wu , Zhiyu Huang , Chao Huang +4 more
Due to the limited smartness and abilities of machine intelligence, currently autonomous vehicles are still unable to handle all kinds of situations and completely replace drivers. Because humans exhibit strong … Due to the limited smartness and abilities of machine intelligence, currently autonomous vehicles are still unable to handle all kinds of situations and completely replace drivers. Because humans exhibit strong robustness and adaptability in complex driving scenarios, it is of great importance to introduce humans into the training loop of artificial intelligence, leveraging human intelligence to further advance machine learning algorithms. In this study, a real-time human-guidance-based deep reinforcement learning (Hug-DRL) method is developed for policy training of autonomous driving. Leveraging a newly designed control transfer mechanism between human and automation, human is able to intervene and correct the agent's unreasonable actions in real time when necessary during the model training process. Based on this human-in-the-loop guidance mechanism, an improved actor-critic architecture with modified policy and value networks is developed. The fast convergence of the proposed Hug-DRL allows real-time human guidance actions to be fused into the agent's training loop, further improving the efficiency and performance of deep reinforcement learning. The developed method is validated by human-in-the-loop experiments with 40 subjects and compared with other state-of-the-art learning approaches. The results suggest that the proposed method can effectively enhance the training efficiency and performance of the deep reinforcement learning algorithm under human guidance, without imposing specific requirements on participant expertise and experience.

Complex Monge-Ampère Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary

2000-10-01
Yang Xing
Abstract We give a characterization of bounded plurisubharmonic functions by using their complex Monge-Ampère measures. This implies a both necessary and sufficient condition for a positive measure to be complex … Abstract We give a characterization of bounded plurisubharmonic functions by using their complex Monge-Ampère measures. This implies a both necessary and sufficient condition for a positive measure to be complex Monge-Ampère measure of some bounded plurisubharmonic function.
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Sufficient conditions for Bayesian consistency

2008-12-01
Yang Xing , Bo Ranneby

Heterogeneous Edge-Enhanced Graph Attention Network For Multi-Agent Trajectory Prediction

2021-01-01
Xiaoyu Mo , Yang Xing , Chen Lv
Simultaneous trajectory prediction for multiple heterogeneous traffic participants is essential for the safe and efficient operation of connected automated vehicles under complex driving situations in the real world. The multi-agent … Simultaneous trajectory prediction for multiple heterogeneous traffic participants is essential for the safe and efficient operation of connected automated vehicles under complex driving situations in the real world. The multi-agent prediction task is challenging, as the motions of traffic participants are affected by many factors, including their individual dynamics, their interactions with surrounding agents, the traffic infrastructures, and the number and modalities of the target agents. To further advance the trajectory prediction techniques, in this work we propose a three-channel framework together with a novel Heterogeneous Edge-enhanced graph ATtention network (HEAT), which is able to deal with the heterogeneity of the target agents and traffic participants involved. Specifically, the agent's dynamics are extracted from their historical states using type-specific encoders. The inter-agent interactions are represented with a directed edge-featured heterogeneous graph, and then interaction features are extracted using the proposed HEAT network. Besides, the map features are shared across all agents by introducing a selective gate mechanism. And finally, the trajectories of multi-agent are executed simultaneously. Validations using both urban and highway driving datasets show that the proposed model can realize simultaneous trajectory predictions for multiple agents under complex traffic situations, and achieve state-of-the-art performance with respect to prediction accuracy, demonstrating its feasibility and effectiveness.
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Convergence in Capacity

2008-01-01
Yang Xing
We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures … We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures which is essentially equivalent to convergence in the capacity C n of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity C n-1 of functions in some case. As applications we give certain stability theorems of solutions of Monge-Ampère equations.
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Weak convergence of currents

2007-11-05
Yang Xing

Continuity of the Complex Monge–Ampère operator on compact Kähler manifolds

2008-09-02
Yang Xing
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On adaptive Bayesian inference

2008-01-01
Yang Xing
We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of … We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general in-probability theorems on the rate of convergence of the resulting posterior distributions. We extend their results to almost sure assertions. As an application we study log spline densities with a finite number of models and obtain that the Bayes procedure achieves the optimal minimax rate n−γ/(2γ+1) of convergence if the true density of the observations belongs to the Hölder space Cγ[0,1]. This strengthens a result in [1; 2]. We also study consistency of posterior distributions of the model index and give conditions ensuring that the posterior distributions concentrate their masses near the index of the best model.
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Convergence rates of nonparametric posterior distributions

2010-10-29
Yang Xing
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A strong comparison principle of plurisubharmonic functions with finite pluricomplex energy

2008-12-01
Yang Xing
A strong comparison principle of plurisubharmonic functions with finite pluricomplex energy A strong comparison principle of plurisubharmonic functions with finite pluricomplex energy
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The complex Monge-Ampere equations with a countable number of singular points

1999-01-01
Yang Xing
We solve the complex Monge-Ampère equation (dd c u) n = µ in a bounded, strictly pseudoconvex domain Ω of C n for certain singular measures µ which may put … We solve the complex Monge-Ampère equation (dd c u) n = µ in a bounded, strictly pseudoconvex domain Ω of C n for certain singular measures µ which may put positive mass at a countable number of points.In particular, we show that any positive measure µ ≤ (dd c v) n is the complex Monge-Ampère measure of some plurisubharmonic function, vanishing on the boundary and being locally bounded outside of a finite number of points, if the plurisubharmonic function v vanishes on the boundary and is locally bounded outside of these points. Introduction.Let Ω be a bounded, strictly pseudoconvex subset in C n .Denote by PSH(Ω) the set of all plurisubharmonic (psh) functions in Ω.We shall use differentiation operators d = ∂ + ∂ and d c = i( ∂ -∂).Following Bedford and Taylor, the complex Monge-Ampère measure (dd c u) n = dd c u ∧ dd c u ∧ ••• ∧ dd c u ( n times ) is a well-defined positive Borel measure for any locally bounded psh function u in Ω.The complex Monge-Ampère operator (dd c ) n is an analogue to the Laplace operator in classical potential theory and plays a great role in pluripotential theory.For interested readers we refer to the very nice and complete surveys of Bedford in [B] and Kiselman in [K1].It is well known that the complex Monge-Ampère operator cannot be applied without problem to all psh functions, e.g., the mass of (dd c u) n of some unbounded psh function may put infinite mass even on a single point, see [K2] or [S].However, the definition of the complex Monge-Ampère measure for locally bounded psh functions can be extended to the important class of psh functions which are locally bounded only near the boundary ∂Ω.From this we have, for instance, that if f = (f 1 ,f 2 ,...,f n ) is a holomorphic map with discrete zero set Z f then (dd c ln |f |) n = (2π) n a∈Z f d f,a δ a ,
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Rates of Posterior Convergence for iid Observations

2010-09-12
Yang Xing
By means of the Hausdorff α-entropy introduced by Xing and Ranneby (2009 Xing , Y. , Ranneby , B. ( 2009 ). Sufficient conditions for Bayesian consistency . J. Statist. … By means of the Hausdorff α-entropy introduced by Xing and Ranneby (2009 Xing , Y. , Ranneby , B. ( 2009 ). Sufficient conditions for Bayesian consistency . J. Statist. Plann. Inference. 139 : 2479 – 2489 .[Crossref] , [Google Scholar]), we give two theorems on rates of in-probability convergence of posterior distributions. The result is applied in study of the Bernstein polynomial priors.

Driving Conditions-Driven Energy Management for Hybrid Electric Vehicles: A Review

2020-01-01
Teng Liu , Xiaolin Tang , Jinwei Zhang +3 more
Motivated by the concerns on transported fuel consumption and global air pollution, industrial engineers, and academic researchers have made many efforts to construct more efficient and environment-friendly vehicles. Hybrid electric … Motivated by the concerns on transported fuel consumption and global air pollution, industrial engineers, and academic researchers have made many efforts to construct more efficient and environment-friendly vehicles. Hybrid electric vehicles (HEVs) are the representative ones because they can satisfy the power demand by coordinating energy supplements among different energy storage devices. To achieve this goal, energy management approaches are crucial technology, and driving cycles are the critical influence factor. Therefore, this paper aims to summarize driving cycle-driven energy management strategies (EMSs) for HEVs. First, the definition and significance of driving cycles in the energy management field are clarified, and the recent literature in this research domain is reviewed and revisited. In addition, according to the known information of driving cycles, the EMSs are divided into three categories, and the relevant study directions, such as standard driving cycles, long-term driving cycle generation (LT-DCG) and short-term driving cycle prediction (ST-DCP) are illuminated and analyzed. Furthermore, the existing database of driving cycles in highway and urban aspects are displayed and discussed. Finally, this article also elaborates on the future prospects of energy management technologies related to driving cycles. This paper focusing on helping the relevant researchers realize the state-of-the-art of HEVs energy management field and also recognize its future development direction.
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A decomposition of complex Monge–Ampère measures

2007-01-01
Yang Xing
We prove a decomposition theorem for complex Monge–Ampère measures of plurisubharmonic functions in connection with their pluripolar sets. We prove a decomposition theorem for complex Monge–Ampère measures of plurisubharmonic functions in connection with their pluripolar sets.
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A Unified Multi-scale and Multi-task Learning Framework for Driver Behaviors Reasoning

2020-01-01
Yang Xing , Chen Lv , Dongpu Cao +1 more
Mutual understanding between driver and vehicle is critically important to the design of intelligent vehicles and customized interaction interface. In this study, a unified driver behavior reasoning system toward multi-scale … Mutual understanding between driver and vehicle is critically important to the design of intelligent vehicles and customized interaction interface. In this study, a unified driver behavior reasoning system toward multi-scale and multi-tasks behavior recognition is proposed. Specifically, a multi-scale driver behavior recognition system is designed to recognize both the driver's physical and mental states based on a deep encoder-decoder framework. This system can jointly recognize three driver behaviors with different time scales based on the shared encoder network. Driver body postures and mental behaviors include intention and emotion are studied and identified. The encoder network is designed based on a deep convolutional neural network (CNN), and several decoders for different driver states estimation are proposed with fully connected (FC) and long short-term memory (LSTM) based recurrent neural networks (RNN). The joint feature learning with the CNN encoder increases the computational efficiency and feature diversity, while the customized decoders enable an efficient multi-tasks inference. The proposed framework can be used as a solution to exploit the relationship between different driver states, and it is found that when drivers generate lane change intentions, their emotions usually keep neutral state and more focus on the task. Two naturalistic datasets are used to investigate the model performance, which is a local highway dataset, namely, CranData and one public dataset from Brain4Cars. The testing results on these two datasets show accurate performance and outperform existing methods on driver postures, intention, and emotion recognition.

Interaction-Aware Trajectory Prediction of Connected Vehicles using CNN-LSTM Networks

2020-01-01
Xiaoyu Mo , Yang Xing
Predicting the future trajectory of a surrounding vehicle in congested traffic is one of the basic abilities of an autonomous vehicle. In congestion, a vehicle's future movement is the result … Predicting the future trajectory of a surrounding vehicle in congested traffic is one of the basic abilities of an autonomous vehicle. In congestion, a vehicle's future movement is the result of its interaction with surrounding vehicles. A vehicle in congestion may have many neighbors in a relatively short distance, while only a small part of neighbors affect its future trajectory mostly. In this work, An interaction-aware method which predicts the future trajectory of an ego vehicle considering its interaction with eight surrounding vehicles is proposed. The dynamics of vehicles are encoded by LSTMs with shared weights, and the interaction is extracted with a simple CNN. The proposed model is trained and tested on trajectories extracted from the publicly accessible NGSIM US-101 dataset. Quantitative experimental results show that the proposed model outperforms previous models in terms of root-mean-square error (RMSE). Results visualization shows that the model is able to predict future trajectory induced by lane change before the vehicle operate obvious lateral movement to initiate lane changing.

Two-Stage Violence Detection Using ViTPose and Classification Models at Smart Airports

2023-08-28
İrem Üstek , Jay Desai , Iván López Torrecillas +7 more
This study introduces an innovative violence detection framework tailored to the unique requirements of smart airports, where prompt responses to violent situations are crucial. The proposed framework harnesses the power … This study introduces an innovative violence detection framework tailored to the unique requirements of smart airports, where prompt responses to violent situations are crucial. The proposed framework harnesses the power of ViTPose for human pose estimation and employs a CNN-BiLSTM network to analyse spatial and temporal information within keypoints sequences, enabling the accurate classification of violent behaviour in real-time. Seamlessly integrated within the SAAB's SAFE (Situational Awareness for Enhanced Security) framework, the solution underwent integrated testing to ensure robust performance in real-world scenarios. The AIRTLab dataset, characterized by its high video quality and relevance to surveillance scenarios, is utilized in this study to enhance the model's accuracy and mitigate false positives. As airports face increased foot traffic in the post-pandemic era, the implementation of AI-driven violence detection systems, such as the one proposed, is paramount for improving security, expediting response times, and promoting data-informed decision-making. The implementation of this framework not only diminishes the probability of violent events but also assists surveillance teams in effectively addressing potential threats, ultimately fostering a more secure and protected aviation sector. Codes are available at: https://github.com/Asami-1/GDP.
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Regular growth of subharmonic functions of several variables.

1993-12-01
Yang Xing
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Convergence Rates of Nonparametric Posterior Distributions

2008-01-01
Yang Xing
We study the asymptotic behavior of posterior distributions. We present general posterior convergence rate theorems, which extend several results on posterior convergence rates provided by Ghosal and Van der Vaart … We study the asymptotic behavior of posterior distributions. We present general posterior convergence rate theorems, which extend several results on posterior convergence rates provided by Ghosal and Van der Vaart (2000), Shen and Wasserman (2001) and Walker, Lijor and Prunster (2007). Our main tools are the Hausdorff $α$-entropy introduced by Xing and Ranneby (2008) and a new notion of prior concentration, which is a slight improvement of the usual prior concentration provided by Ghosal and Van der Vaart (2000). We apply our results to several statistical models.

The General Definition of the Complex Monge-Ampère Operator on Compact Kähler Manifolds

2007-01-01
Yang Xing
We introduce a wide subclass ${\cal F}(X,\omega)$ of quasi-plurisubharmonic functions in a compact K\"ahler manifold, on which the complex Monge-Amp\`ere operator is well-defined and the convergence theorem is valid. We … We introduce a wide subclass ${\cal F}(X,\omega)$ of quasi-plurisubharmonic functions in a compact K\"ahler manifold, on which the complex Monge-Amp\`ere operator is well-defined and the convergence theorem is valid. We also prove that ${\cal F}(X,\omega)$ is a convex cone and includes all quasi-plurisubharmonic functions which are in the Cegrell class.
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Human-Machine Collaboration for Automated Vehicles via an Intelligent Two-Phase Haptic Interface

2020-01-01
Chen Lv , Yutong Li , Yang Xing +4 more
Prior to realizing fully autonomous driving, human intervention will be required periodically to guarantee vehicle safety. This fact poses a new challenge in human-machine interaction, particularly during control authority transition … Prior to realizing fully autonomous driving, human intervention will be required periodically to guarantee vehicle safety. This fact poses a new challenge in human-machine interaction, particularly during control authority transition from the automated functionality to a human driver. This paper addresses this challenge by proposing an intelligent haptic interface based on a newly developed two-phase human-machine interaction model. The intelligent haptic torque is applied on the steering wheel and switches its functionality between predictive guidance and haptic assistance according to the varying state and control ability of human drivers, helping drivers gradually resume manual control during takeover. The developed approach is validated by conducting vehicle experiments with 26 human participants. The results suggest that the proposed method can effectively enhance the driving state recovery and control performance of human drivers during takeover compared with an existing approach, further improving the safety and smoothness of the human-machine interaction in automated vehicles.
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Multi-task Driver Steering Behaviour Modeling Using Time-Series Transformer

2022-01-01
Yang Xing , Wenbo Li , Xiaoyu Mo +1 more
Human intention prediction provides an augmented solution for the design of assistants and collaboration between the human driver and intelligent vehicles. In this study, a multi-task sequential learning framework is … Human intention prediction provides an augmented solution for the design of assistants and collaboration between the human driver and intelligent vehicles. In this study, a multi-task sequential learning framework is developed to predict future steering torques and steering postures based on the upper limb neuromuscular Electromyography (EMG) signals. A single-right-hand driving mode is particularly studied. For this driving mode, three different driving postures are also evaluated. Then, a multi-task time-series transformer network (MTS-Trans) is developed to predict the steering torques and driving postures. To evaluate the multi-task learning performance, four different frameworks are assessed. Twenty-one participants are involved in the driving simulator-based experiment. The proposed model achieved accurate prediction results on the future steering torque prediction and driving postures recognition for single-hand driving modes. The proposed system can contribute to the development of advanced driver steering assistant systems and ensure mutual understanding between human drivers and intelligent vehicles.

Explainable Interface for Human-Autonomy Teaming: A Survey

2024-05-04
Xiangqi Kong , Yang Xing , Antonios Tsourdos +4 more
Nowadays, large-scale foundation models are being increasingly integrated into numerous safety-critical applications, including human-autonomy teaming (HAT) within transportation, medical, and defence domains. Consequently, the inherent 'black-box' nature of these sophisticated … Nowadays, large-scale foundation models are being increasingly integrated into numerous safety-critical applications, including human-autonomy teaming (HAT) within transportation, medical, and defence domains. Consequently, the inherent 'black-box' nature of these sophisticated deep neural networks heightens the significance of fostering mutual understanding and trust between humans and autonomous systems. To tackle the transparency challenges in HAT, this paper conducts a thoughtful study on the underexplored domain of Explainable Interface (EI) in HAT systems from a human-centric perspective, thereby enriching the existing body of research in Explainable Artificial Intelligence (XAI). We explore the design, development, and evaluation of EI within XAI-enhanced HAT systems. To do so, we first clarify the distinctions between these concepts: EI, explanations and model explainability, aiming to provide researchers and practitioners with a structured understanding. Second, we contribute to a novel framework for EI, addressing the unique challenges in HAT. Last, our summarized evaluation framework for ongoing EI offers a holistic perspective, encompassing model performance, human-centered factors, and group task objectives. Based on extensive surveys across XAI, HAT, psychology, and Human-Computer Interaction (HCI), this review offers multiple novel insights into incorporating XAI into HAT systems and outlines future directions.
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Cooperative Driving of Connected Autonomous Vehicles in Heterogeneous Mixed Traffic: A Game Theoretic Approach

2024-01-01
Shiyu Fang , Peng Hang , Chongfeng Wei +2 more
High-density, unsignalized intersections have always been a bottleneck of efficiency and safety.The emergence of Connected Autonomous Vehicles (CAVs) results in a mixed traffic condition, further increasing the complexity of the … High-density, unsignalized intersections have always been a bottleneck of efficiency and safety.The emergence of Connected Autonomous Vehicles (CAVs) results in a mixed traffic condition, further increasing the complexity of the transportation system.Against this background, this paper aims to study the intricate and heterogeneous interaction of vehicles and conflict resolution at the high-density, mixed, unsignalized intersection.Theoretical insights about the interaction between CAVs and Human-driven Vehicles (HVs) and the cooperation of CAVs are synthesized, based on which a novel cooperative decisionmaking framework in heterogeneous mixed traffic is proposed.Normalized Cooperative game is concatenated with Level-k game (NCL game) to generate a system optimal solution.Then Lattice planner generates the optimal and collision-free trajectories for CAVs.To reproduce HVs in mixed traffic, interactions from naturalistic human driving data are extracted as prior knowledge.Non-cooperative game and Inverse Reinforcement Learning (IRL) are integrated to mimic the decision-making of heterogeneous HVs.Finally, three cases are conducted to verify the performance of the proposed algorithm, including the comparative analysis with different methods, the case study under different Rates of Penetration (ROP) and the interaction analysis with heterogeneous HVs.It is found that the proposed cooperative decision-making framework is beneficial to driving conflict resolution and the traffic efficiency improvement of the mixed unsignalized intersection.Besides, due to the consideration of driving heterogeneity, better human-machine interaction and cooperation can be realized in this paper.
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Both necessary and sufficient conditions for Bayesian exponential consistency

2008-01-01
Yang Xing , Bo Ranneby
The last decade has seen a remarkable development in the theory of asymptotics of Bayesian nonparametric procedures. Exponential consistency has played an important role in this area. It is known … The last decade has seen a remarkable development in the theory of asymptotics of Bayesian nonparametric procedures. Exponential consistency has played an important role in this area. It is known that the condition of $f_0$ being in the Kullback-Leibler support of the prior cannot ensure exponential consistency of posteriors. Many authors have obtained additional sufficient conditions for exponential consistency of posteriors, see, for instance, Schwartz (1965), Barron, Schervish and Wasserman (1999), Ghosal, Ghosh and Ramamoorthi (1999), Walker (2004), Xing and Ranneby (2008). However, given the Kullback-Leibler support condition, less is known about both necessary and sufficient conditions. In this paper we give one type of both necessary and sufficient conditions. As a consequence we derive a simple sufficient condition on Bayesian exponential consistency, which is weaker than the previous sufficient conditions.

On strong Hellinger consistency of posterior distributions

2012-02-02
Yang Xing , Bo Ranneby
Abstract We establish a sufficient condition ensuring strong Hellinger consistency of posterior distributions. We also prove a strong Hellinger consistency theorem for the pseudoposterior distributions based on the likelihood ratio … Abstract We establish a sufficient condition ensuring strong Hellinger consistency of posterior distributions. We also prove a strong Hellinger consistency theorem for the pseudoposterior distributions based on the likelihood ratio with power 0<α<1, which are introduced by Walker and Hjort [2001 ‘On Bayesian Consistency’, J. R. Statist. Soc., B 63, 811–821]. Our result is an extension of their theorem for α=½. Keywords: Hellinger consistencyposterior distributionnonparametric model AMS 2000 Subject Classifications:: 62G0762G2062F15 Acknowledgements We are grateful to an associate editor and two anonymous referees for their helpful comments and suggestions.

The General Definition of the Complex Monge–Ampère Operator on Compact Kähler Manifolds

2009-12-22
Yang Xing
Abstract We introduce a wide subclass of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well defined and the convergence theorem is valid. We … Abstract We introduce a wide subclass of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well defined and the convergence theorem is valid. We also prove that is a convex cone and includes all quasi-plurisubharmonic functions that are in the Cegrell class.
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Subharmonic functions of completely regular growth in a cone

1994-10-01
Yang Xing
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Human-Like Decision Making for Autonomous Driving: A Noncooperative Game Theoretic Approach

2020-01-01
Peng Hang , Chen Lv , Yang Xing +2 more
Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers traffic ecology and minimize … Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers traffic ecology and minimize the effect of AVs and their misfit with human drivers, are issues worthy of consideration. Moreover, different passengers have different needs for AVs, thus, how to provide personalized choices for different passengers is another issue for AVs. Therefore, a human-like decision making framework is designed for AVs in this paper. Different driving styles and social interaction characteristics are formulated for AVs regarding driving safety, ride comfort and travel efficiency, which are considered in the modeling process of decision making. Then, Nash equilibrium and Stackelberg game theory are applied to the noncooperative decision making. In addition, potential field method and model predictive control (MPC) are combined to deal with the motion prediction and planning for AVs, which provides predicted motion information for the decision-making module. Finally, two typical testing scenarios of lane change, i.e., merging and overtaking, are carried out to evaluate the feasibility and effectiveness of the proposed decision-making framework considering different human-like behaviors. Testing results indicate that both the two game theoretic approaches can provide reasonable human-like decision making for AVs. Compared with the Nash equilibrium approach, under the normal driving style, the cost value of decision making using the Stackelberg game theoretic approach is reduced by over 20%.
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Defining Digital Quadruplets in the Cyber-Physical-Social Space for Parallel Driving

2020-01-01
Teng Liu , Yang Xing , Long Chen +2 more
Parallel driving is a novel framework to synthesize vehicle intelligence and transport automation. This article aims to define digital quadruplets in parallel driving. In the cyber-physical-social systems (CPSS), based on … Parallel driving is a novel framework to synthesize vehicle intelligence and transport automation. This article aims to define digital quadruplets in parallel driving. In the cyber-physical-social systems (CPSS), based on the ACP method, the names of the digital quadruplets are first given, which are descriptive, predictive, prescriptive and real vehicles. The objectives of the three virtual digital vehicles are interacting, guiding, simulating and improving with the real vehicles. Then, the three virtual components of the digital quadruplets are introduced in detail and their applications are also illustrated. Finally, the real vehicles in the parallel driving system and the research process of the digital quadruplets are depicted. The presented digital quadruplets in parallel driving are expected to make the future connected automated driving safety, efficiently and synergistically.

Human-Machine Adaptive Shared Control for Safe Automated Driving under Automation Degradation

2021-01-01
Chao Huang , Chen Lv , Peng Hang +2 more
In this paper, a human-machine adaptive shared control method is proposed for automated vehicles (AVs) under automation performance degradation. First, a novel risk assessment module is proposed to monitor driving … In this paper, a human-machine adaptive shared control method is proposed for automated vehicles (AVs) under automation performance degradation. First, a novel risk assessment module is proposed to monitor driving behavior and evaluate automation performance degradation for AVs. Then, an adaptive control authority allocation module is developed. In the event of any performance degradation detection, the allocated control authority of the automation system is decreased based on the assessed risk to reduce the potential risk of vehicle motion. Consequently, the control authority allocated to the human driver is adaptively increased and thus requires more driver engagement in the control loop to compensate for the automation degradation and ensure AV safety. Experimental validation is conducted under different driving scenarios. The testing results show that the proposed approach is able to effectively compensate for the performance degradation of vehicle automation through the human-machine adaptive shared control, ensuring the safety of automated driving

Cooperative Decision Making of Connected Automated Vehicles at Multi-lane Merging Zone: A Coalitional Game Approach

2021-01-01
Peng Hang , Chen Lv , Chao Huang +2 more
To address the safety and efficiency issues of vehicles at multi-lane merging zones, a cooperative decision-making framework is designed for connected automated vehicles (CAVs) using a coalitional game approach. Firstly, … To address the safety and efficiency issues of vehicles at multi-lane merging zones, a cooperative decision-making framework is designed for connected automated vehicles (CAVs) using a coalitional game approach. Firstly, a motion prediction module is established based on the simplified single-track vehicle model for enhancing the accuracy and reliability of the decision-making algorithm. Then, the cost function and constraints of the decision making are designed considering multiple performance indexes, i.e. the safety, comfort and efficiency. Besides, in order to realize human-like and personalized smart mobility, different driving characteristics are considered and embedded in the modeling process. Furthermore, four typical coalition models are defined for CAVS at the scenario of a multi-lane merging zone. Then, the coalitional game approach is formulated with model predictive control (MPC) to deal with decision making of CAVs at the defined scenario. Finally, testings are carried out in two cases considering different driving characteristics to evaluate the performance of the developed approach. The testing results show that the proposed coalitional game based method is able to make reasonable decisions and adapt to different driving characteristics for CAVs at the multi-lane merging zone. It guarantees the safety and efficiency of CAVs at the complex dynamic traffic condition, and simultaneously accommodates the objectives of individual vehicles, demonstrating the feasibility and effectiveness of the proposed approach.

Vision-based Conflict Detection within Crowds based on High-Resolution Human Pose Estimation for Smart and Safe Airport

2022-01-01
Karan Kheta , Claire Delgove , Ruolin Liu +5 more
Future airports are becoming more complex and congested with the increasing number of travellers. While the airports are more likely to become hotspots for potential conflicts to break out which … Future airports are becoming more complex and congested with the increasing number of travellers. While the airports are more likely to become hotspots for potential conflicts to break out which can cause serious delays to flights and several safety issues. An intelligent algorithm which renders security surveillance more effective in detecting conflicts would bring many benefits to the passengers in terms of their safety, finance, and travelling efficiency. This paper details the development of a machine learning model to classify conflicting behaviour in a crowd. HRNet is used to segment the images and then two approaches are taken to classify the poses of people in the frame via multiple classifiers. Among them, it was found that the support vector machine (SVM) achieved the most performant achieving precision of 94.37%. Where the model falls short is against ambiguous behaviour such as a hug or losing track of a subject in the frame. The resulting model has potential for deployment within an airport if improvements are made to cope with the vast number of potential passengers in view as well as training against further ambiguous behaviours which will arise in an airport setting. In turn, will provide the capability to enhance security surveillance and improve airport safety.

Zeros and growth of entire functions of several variables, the complex Monge-Ampere operator and some related topics

1992-01-01
Yang Xing
The classical Levin-Pfluger theory of entire functions of completely regular growth ($CRG$) of finite order $\rho$ in one variable establishes a relation between the distribution of zeros of an entire … The classical Levin-Pfluger theory of entire functions of completely regular growth ($CRG$) of finite order $\rho$ in one variable establishes a relation between the distribution of zeros of an entire function and its growth. The most important and interesting result in this theory is the fundamental principle for $CRG$ functions. In the book of Gruman and Lelong, this basic theorem was generalized to entire functions of several variables. In this theorem the additional hypotheses have to be made for integral order $\rho$. We prove one common characterization for any $\rho$. As an application we prove the following fact: $ r^{-\rho} \log |f(rz)|$ converges to the indicator function $h^\ast_f(z)$ as a distribution if and only if $r^{-\rho} \Delta\log |f(rz)|$ converges to $\Delta h^\ast_f(z)$ as a distribution. This also strengthens a result of Azarin. Lelong has shown that the indicator $h^\ast_f$ is no longer continuous in several variables. But Gruman and Berndtsson have proved that $h^\ast_f$ is continuous if the density of the zero set of $f$ is very small. We relax their conditions. We also get a characterization of regular growth functions with continuous indicators. Moreover, we characterize several kinds of limit sets in the sense of Azarin. For subharmonic $CRG$ functions in a cone, the situation is much different from functions defined in the whole space. We introduce a new definition for $CRG$ functions in a cone. We also give new criteria for functions to be $CRG$ in an open cone, and strengthen some results due to Ronkin. Furthermore, we study $CRG$ functions in a closed cone. It was proved by Bedford and Taylor that the complex Monge-Amp\`ere operator $(dd^c)^q$ is continuous under monotone limits. Cegrell and Lelong showed that the monotonicity hypothesis is essential. Improving a result of Ronkin, we get that $(dd^c)^q$ is continuous under almost uniform limits with respect to Hausdorff $\alpha$-content. Moreover, we study the Dirichlet problem for the complex Monge-Amp\`ere operator. Finally, we confirm a conjecture of Bloom on a generalization of the M\untz-Sz\'asz theorem to several variables. (Less)

Convergence rates of posterior distributions for observations without the iid structure

2008-01-01
Yang Xing
The classical condition on the existence of uniformly exponentially consistent tests for testing the true density against the complement of its arbitrary neighborhood has been widely adopted in study of … The classical condition on the existence of uniformly exponentially consistent tests for testing the true density against the complement of its arbitrary neighborhood has been widely adopted in study of asymptotics of Bayesian nonparametric procedures. Because we follow a Bayesian approach, it seems to be more natural to explore alternative and appropriate conditions which incorporate the prior distribution. In this paper we supply a new prior-dependent integration condition to establish general posterior convergence rate theorems for observations which may not be independent and identically distributed. The posterior convergence rates for such observations have recently studied by Ghosal and van der Vaart \cite{ghv1}. We moreover adopt the Hausdorff $α$-entropy given by Xing and Ranneby \cite{xir1}\cite{xi1}, which is also prior-dependent and smaller than the widely used metric entropies. These lead to extensions of several existing theorems. In particular, we establish a posterior convergence rate theorem for general Markov processes and as its application we improve on the currently known posterior rate of convergence for a nonlinear autoregressive model.

A Universal Prior Distribution for Bayesian Consistency of Non parametric Procedures

2015-03-04
Yang Xing
The introduction of the Hausdorff α-entropy in Xing (2008a Xing, Y. (2008a). Convergence rates of posterior distributions for observations without the iid structure, 38 pages. Available at: www.arxiv.org:0811.4677v1. [Google Scholar]), … The introduction of the Hausdorff α-entropy in Xing (2008a Xing, Y. (2008a). Convergence rates of posterior distributions for observations without the iid structure, 38 pages. Available at: www.arxiv.org:0811.4677v1. [Google Scholar]), Xing (2008b Xing, Y. (2008b). On adaptive Bayesian inference. Electron. J. Stat. 2:848–862.[Crossref] , [Google Scholar]), Xing (2010 Xing, Y. (2010). Rates of posterior convergence for iid Observations. Commun. Stat. Theory Methods. 39(19):3389–3398.[Taylor & Francis Online] , [Google Scholar]), Xing (2011 Xing, Y. (2011). Convergence rates of nonparametric posterior distributions. J. Stat. Plann. Inference 141:3382–3390.[Crossref], [Web of Science ®] , [Google Scholar]), and Xing and Ranneby (2009 Xing, Y., Ranneby, B. (2009). Sufficient conditions for Bayesian consistency. J. Stat. Plann. Inference. 139:2479–2489.[Crossref], [Web of Science ®] , [Google Scholar]) has lead a series of improvements of well-known results on posterior consistency. In this paper we discuss an application of the Hausdorff α-entropy. We construct a universal prior distribution such that the corresponding posterior distribution is almost surely consistent. The approach of the construction of this type of prior distribution is natural, but it works very well for all separable models. We illustrate such prior distributions by examples. In particular, we obtain that if the true density function is known to be some normal probability density function with unknown mean and unknown variance then without any additional assumption one can construct a prior distribution which leads to posterior consistency.

Operation of fermat's last theorem

2008-01-01
Yang Xing
Pierre de Fermat first mentioned this world-known theorem.It will be perfect if we find out the clever operation.This study managed to work out the ingenious operation from the specific to … Pierre de Fermat first mentioned this world-known theorem.It will be perfect if we find out the clever operation.This study managed to work out the ingenious operation from the specific to general methods by using elementary mathematics knowledge.The equation xn+yn=zn(n2)(The letters are all positive integer except especially mentioned) was proven by quadratic equation.when x=10a,z does not equal positive integer.From this,we can get the conclusion 1 adds the rational number n power of exponent and n root is the irrational number.So we get the very method in this way.

An MLE analysis on the relationship between the initial-state granularity and final-state flow factorization

2025-05-10
Shuifa Shen , Chong Ye , Dan Wen +5 more
Abstract In this study, we employ the maximum likelihood estimator (MLE) to investigate the relationship between initial-state fluctuations and final-state anisotropies in relativistic heavy-ion collisions.&amp;#xD;The granularity of the initial state, … Abstract In this study, we employ the maximum likelihood estimator (MLE) to investigate the relationship between initial-state fluctuations and final-state anisotropies in relativistic heavy-ion collisions.&amp;#xD;The granularity of the initial state, reflecting fluctuations in the initial conditions (IC), is modeled using a peripheral tube model.&amp;#xD;Besides differential flow, our analysis focuses on a class of more sensitive observables known as flow factorization.&amp;#xD;Specifically, we evaluate these observables using MLE, an asymptotically normal and unbiased tool in standard statistical inference.&amp;#xD;Our findings show that the resulting differential flow remains essentially unchanged for different IC defined by the peripheral tube model.&amp;#xD;The resulting harmonic coefficients obtained using MLE and multi-particle cumulants are found to be consistent.&amp;#xD;However, the calculated flow factorizations show significant variations depending on both the IC and the estimators, which is attributed to their sensitivity to initial-state fluctuations.&amp;#xD;Thus, we argue that MLE offers a compelling alternative to standard methods such as multi-particle correlators, particularly for sensitive observables constructed from higher moments of the azimuthal distribution.

An MLE analysis on the relationship between the initial-state granularity and final-state flow factorization

2025-02-08
Shuifa Shen , Chong Ye , Dan Wen +5 more
In this study, we employ the maximum likelihood estimator (MLE) to investigate the relationship between initial-state fluctuations and final-state anisotropies in relativistic heavy-ion collisions. The granularity of the initial state, … In this study, we employ the maximum likelihood estimator (MLE) to investigate the relationship between initial-state fluctuations and final-state anisotropies in relativistic heavy-ion collisions. The granularity of the initial state, reflecting fluctuations in the initial conditions (IC), is modeled using a peripheral tube model. Besides differential flow, our analysis focuses on a class of more sensitive observables known as flow factorization. Specifically, we evaluate these observables using MLE, an asymptotically normal and unbiased tool in standard statistical inference. Our findings show that the resulting differential flow remains essentially unchanged for different IC defined by the peripheral tube model. The resulting harmonic coefficients obtained using MLE and multi-particle cumulants are found to be consistent. However, the calculated flow factorizations show significant variations depending on both the IC and the estimators, which is attributed to their sensitivity to initial-state fluctuations. Thus, we argue that MLE offers a compelling alternative to standard methods such as multi-particle correlators, particularly for sensitive observables constructed from higher moments of the azimuthal distribution.
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Topological selective non hermitian skin effect

2025-01-01
Yang Xing , LIU Mengjiao , HOU Jiahao +2 more
Topologically protected waveguides have attracted growing interest due to their robustness against disorder and defects. In parallel, the advent of non-Hermitian physics—with its inherent gain-and-loss mechanisms—has introduced new tools for … Topologically protected waveguides have attracted growing interest due to their robustness against disorder and defects. In parallel, the advent of non-Hermitian physics—with its inherent gain-and-loss mechanisms—has introduced new tools for manipulating wave localization and transport. However, most attempts to combine non-Hermitian effects with topological systems impose the non-Hermitian skin effect (NHSE) uniformly on all modes, lacking selectivity for topological states.&lt;br&gt;In this work, we propose a scheme that realizes a topologically selective NHSE by combining sub-symmetry-protected boundary modes with long-range, non-reciprocal couplings. In a modified Su–Schrieffer–Heeger (SSH) chain, we analytically demonstrate that even in a spectrum densely populated with bulk states, a robust zero-energy edge mode can be preserved while the NHSE is selectively applied to the trivial bulk modes, achieving spatial separation between topological and bulk states. By tuning the long-range couplings, we observe a non-Hermitian phase transition in the complex energy spectrum: it evolves from a closed loop (circle), to an arc, and then to a loop with reversed winding direction. These transitions correspond to a leftward NHSE, the disappearance of the NHSE, and a rightward NHSE, respectively. Calculating the generalized Brillouin zone (GBZ), we confirm this transition by observing the GBZ crossing the unit circle, indicating a change in the NHSE direction.&lt;br&gt;We further extend our model to a two-dimensional higher-order SSH lattice, where selective non-Hermitian modulation enables clear spatial separation between topological corner states and bulk modes. To quantify this, we compute the local density of states (LDOS) in the complex energy plane for site 0 (a topologically localized corner) and site 288 (a region exhibiting NHSE). The LDOS comparison reveals that the topological states are primarily localized at site 0, while bulk states affected by NHSE accumulate at site 288.&lt;br&gt;To validate the theoretical predictions, we perform finite-element simulations of optical resonator arrays employing whispering-gallery modes. By tuning the coupling distances and incorporating gain/loss through refractive index engineering, we replicate the modified SSH model and confirm the selective localization of topological and bulk modes.&lt;br&gt;Our results demonstrate a robust method for the selective excitation and spatial control of topological states in non-Hermitian systems, providing a foundation for future low-crosstalk, high-stability topological photonic devices.

Automating Emergency Landing in Cities with Cognitive Stress Reducing Explanations to Pilot-In-The-Loop

2024-10-29
Hamsa Balakrishnan , Bastien Lechardoy , Maxime Collignon +7 more

Explainable Interface for Human-Autonomy Teaming: A Survey

2024-05-04
Xiangqi Kong , Yang Xing , Antonios Tsourdos +4 more
Nowadays, large-scale foundation models are being increasingly integrated into numerous safety-critical applications, including human-autonomy teaming (HAT) within transportation, medical, and defence domains. Consequently, the inherent 'black-box' nature of these sophisticated … Nowadays, large-scale foundation models are being increasingly integrated into numerous safety-critical applications, including human-autonomy teaming (HAT) within transportation, medical, and defence domains. Consequently, the inherent 'black-box' nature of these sophisticated deep neural networks heightens the significance of fostering mutual understanding and trust between humans and autonomous systems. To tackle the transparency challenges in HAT, this paper conducts a thoughtful study on the underexplored domain of Explainable Interface (EI) in HAT systems from a human-centric perspective, thereby enriching the existing body of research in Explainable Artificial Intelligence (XAI). We explore the design, development, and evaluation of EI within XAI-enhanced HAT systems. To do so, we first clarify the distinctions between these concepts: EI, explanations and model explainability, aiming to provide researchers and practitioners with a structured understanding. Second, we contribute to a novel framework for EI, addressing the unique challenges in HAT. Last, our summarized evaluation framework for ongoing EI offers a holistic perspective, encompassing model performance, human-centered factors, and group task objectives. Based on extensive surveys across XAI, HAT, psychology, and Human-Computer Interaction (HCI), this review offers multiple novel insights into incorporating XAI into HAT systems and outlines future directions.
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Cooperative Driving of Connected Autonomous Vehicles in Heterogeneous Mixed Traffic: A Game Theoretic Approach

2024-01-01
Shiyu Fang , Peng Hang , Chongfeng Wei +2 more
High-density, unsignalized intersections have always been a bottleneck of efficiency and safety.The emergence of Connected Autonomous Vehicles (CAVs) results in a mixed traffic condition, further increasing the complexity of the … High-density, unsignalized intersections have always been a bottleneck of efficiency and safety.The emergence of Connected Autonomous Vehicles (CAVs) results in a mixed traffic condition, further increasing the complexity of the transportation system.Against this background, this paper aims to study the intricate and heterogeneous interaction of vehicles and conflict resolution at the high-density, mixed, unsignalized intersection.Theoretical insights about the interaction between CAVs and Human-driven Vehicles (HVs) and the cooperation of CAVs are synthesized, based on which a novel cooperative decisionmaking framework in heterogeneous mixed traffic is proposed.Normalized Cooperative game is concatenated with Level-k game (NCL game) to generate a system optimal solution.Then Lattice planner generates the optimal and collision-free trajectories for CAVs.To reproduce HVs in mixed traffic, interactions from naturalistic human driving data are extracted as prior knowledge.Non-cooperative game and Inverse Reinforcement Learning (IRL) are integrated to mimic the decision-making of heterogeneous HVs.Finally, three cases are conducted to verify the performance of the proposed algorithm, including the comparative analysis with different methods, the case study under different Rates of Penetration (ROP) and the interaction analysis with heterogeneous HVs.It is found that the proposed cooperative decision-making framework is beneficial to driving conflict resolution and the traffic efficiency improvement of the mixed unsignalized intersection.Besides, due to the consideration of driving heterogeneity, better human-machine interaction and cooperation can be realized in this paper.
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Two-Stage Violence Detection Using ViTPose and Classification Models at Smart Airports

2023-08-28
İrem Üstek , Jay Desai , Iván López Torrecillas +7 more
This study introduces an innovative violence detection framework tailored to the unique requirements of smart airports, where prompt responses to violent situations are crucial. The proposed framework harnesses the power … This study introduces an innovative violence detection framework tailored to the unique requirements of smart airports, where prompt responses to violent situations are crucial. The proposed framework harnesses the power of ViTPose for human pose estimation and employs a CNN-BiLSTM network to analyse spatial and temporal information within keypoints sequences, enabling the accurate classification of violent behaviour in real-time. Seamlessly integrated within the SAAB's SAFE (Situational Awareness for Enhanced Security) framework, the solution underwent integrated testing to ensure robust performance in real-world scenarios. The AIRTLab dataset, characterized by its high video quality and relevance to surveillance scenarios, is utilized in this study to enhance the model's accuracy and mitigate false positives. As airports face increased foot traffic in the post-pandemic era, the implementation of AI-driven violence detection systems, such as the one proposed, is paramount for improving security, expediting response times, and promoting data-informed decision-making. The implementation of this framework not only diminishes the probability of violent events but also assists surveillance teams in effectively addressing potential threats, ultimately fostering a more secure and protected aviation sector. Codes are available at: https://github.com/Asami-1/GDP.
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Milestones in Autonomous Driving and Intelligent Vehicles—Part I: Control, Computing System Design, Communication, HD Map, Testing, and Human Behaviors

2023-05-29
Long Chen , Yuchen Li , Chao Huang +7 more
Interest in autonomous driving (AD) and intelligent vehicles (IVs) is growing at a rapid pace due to the convenience, safety, and economic benefits. Although a number of surveys have reviewed … Interest in autonomous driving (AD) and intelligent vehicles (IVs) is growing at a rapid pace due to the convenience, safety, and economic benefits. Although a number of surveys have reviewed research achievements in this field, they are still limited in specific tasks and lack systematic summaries and research directions in the future. Our work is divided into three independent articles and the first part is a survey of surveys (SoS) for total technologies of AD and IVs that involves the history, summarizes the milestones, and provides the perspectives, ethics, and future research directions. This is the second part (Part I for this technical survey) to review the development of control, computing system design, communication, high-definition map (HD map), testing, and human behaviors in IVs. In addition, the third part (Part II for this technical survey) is to review the perception and planning sections. The objective of this article is to involve all the sections of AD, summarize the latest technical milestones, and guide abecedarians to quickly understand the development of AD and IVs. Combining the SoS and Part II, we anticipate that this work will bring novel and diverse insights to researchers and abecedarians, and serve as a bridge between past and future.
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Two-Stage Violence Detection Using ViTPose and Classification Models at Smart Airports

2023-01-01
İrem Üstek , Jay Desai , Iván López Torrecillas +7 more
This study introduces an innovative violence detection framework tailored to the unique requirements of smart airports, where prompt responses to violent situations are crucial. The proposed framework harnesses the power … This study introduces an innovative violence detection framework tailored to the unique requirements of smart airports, where prompt responses to violent situations are crucial. The proposed framework harnesses the power of ViTPose for human pose estimation. It employs a CNN - BiLSTM network to analyse spatial and temporal information within keypoints sequences, enabling the accurate classification of violent behaviour in real time. Seamlessly integrated within the SAFE (Situational Awareness for Enhanced Security framework of SAAB, the solution underwent integrated testing to ensure robust performance in real world scenarios. The AIRTLab dataset, characterized by its high video quality and relevance to surveillance scenarios, is utilized in this study to enhance the model's accuracy and mitigate false positives. As airports face increased foot traffic in the post pandemic era, implementing AI driven violence detection systems, such as the one proposed, is paramount for improving security, expediting response times, and promoting data informed decision making. The implementation of this framework not only diminishes the probability of violent events but also assists surveillance teams in effectively addressing potential threats, ultimately fostering a more secure and protected aviation sector. Codes are available at: https://github.com/Asami-1/GDP.

Milestones in Autonomous Driving and Intelligent Vehicles: Survey of Surveys

2022-11-24
Long Chen , Yuchen Li , Chao Huang +7 more
Interest in autonomous driving (AD) and intelligent vehicles (IVs) is growing at a rapid pace due to the convenience, safety, and economic benefits. Although a number of surveys have reviewed … Interest in autonomous driving (AD) and intelligent vehicles (IVs) is growing at a rapid pace due to the convenience, safety, and economic benefits. Although a number of surveys have reviewed research achievements in this field, they are still limited in specific tasks, lack of systematic summary and research directions in the future. Here we propose a Survey of Surveys (SoS) for total technologies of AD and IVs that reviews the history, summarizes the milestones, and provides the perspectives, ethics, and future research directions. To our knowledge, this article is the first SoS with milestones in AD and IVs, which constitutes our complete research work together with two other technical surveys. We anticipate that this article will bring novel and diverse insights to researchers and abecedarians, and serve as a bridge between past and future.
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Reducing Viral Transmission through AI-based Crowd Monitoring and Social Distancing Analysis

2022-09-20
Benjamin T. Fraser , Brendan Copp , Gurpreet Singh +6 more
This paper explores multi-person pose estimation for reducing the risk of airborne pathogens. The recent COVID-19 pandemic highlights these risks in a globally connected world. We developed several techniques which … This paper explores multi-person pose estimation for reducing the risk of airborne pathogens. The recent COVID-19 pandemic highlights these risks in a globally connected world. We developed several techniques which analyse CCTV inputs for crowd analysis. The framework utilised automated homography from pose feature positions to determine interpersonal distance. It also incorporates mask detection by using pose features for an image classification pipeline. A further model predicts the behaviour of each person by using their estimated pose features. We combine the models to assess transmission risk based on recent scientific literature. A custom dashboard displays a risk density heat-map in real time. This system could improve public space management and reduce transmission in future pandemics. This context agnostic system and has many applications for other crowd monitoring problems.
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A posterior convergence rate theorem for general Markov chains

2022-02-08
Yang Xing
This paper establishes a posterior convergence rate theorem for general Markov chains. Our approach is based on the Hausdorff α-entropy introduced by Xing (Electronic Journal of Statistics 2:848–62, 2008) and … This paper establishes a posterior convergence rate theorem for general Markov chains. Our approach is based on the Hausdorff α-entropy introduced by Xing (Electronic Journal of Statistics 2:848–62, 2008) and Xing and Ranneby (Journal of Statistical Planning and Inference 139 (7):2479–89, 2009). As an application we illustrate our results on a non linear autoregressive model.
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Multi-task Driver Steering Behaviour Modeling Using Time-Series Transformer

2022-01-01
Yang Xing , Wenbo Li , Xiaoyu Mo +1 more
Human intention prediction provides an augmented solution for the design of assistants and collaboration between the human driver and intelligent vehicles. In this study, a multi-task sequential learning framework is … Human intention prediction provides an augmented solution for the design of assistants and collaboration between the human driver and intelligent vehicles. In this study, a multi-task sequential learning framework is developed to predict future steering torques and steering postures based on the upper limb neuromuscular Electromyography (EMG) signals. A single-right-hand driving mode is particularly studied. For this driving mode, three different driving postures are also evaluated. Then, a multi-task time-series transformer network (MTS-Trans) is developed to predict the steering torques and driving postures. To evaluate the multi-task learning performance, four different frameworks are assessed. Twenty-one participants are involved in the driving simulator-based experiment. The proposed model achieved accurate prediction results on the future steering torque prediction and driving postures recognition for single-hand driving modes. The proposed system can contribute to the development of advanced driver steering assistant systems and ensure mutual understanding between human drivers and intelligent vehicles.

Vision-based Conflict Detection within Crowds based on High-Resolution Human Pose Estimation for Smart and Safe Airport

2022-01-01
Karan Kheta , Claire Delgove , Ruolin Liu +5 more
Future airports are becoming more complex and congested with the increasing number of travellers. While the airports are more likely to become hotspots for potential conflicts to break out which … Future airports are becoming more complex and congested with the increasing number of travellers. While the airports are more likely to become hotspots for potential conflicts to break out which can cause serious delays to flights and several safety issues. An intelligent algorithm which renders security surveillance more effective in detecting conflicts would bring many benefits to the passengers in terms of their safety, finance, and travelling efficiency. This paper details the development of a machine learning model to classify conflicting behaviour in a crowd. HRNet is used to segment the images and then two approaches are taken to classify the poses of people in the frame via multiple classifiers. Among them, it was found that the support vector machine (SVM) achieved the most performant achieving precision of 94.37%. Where the model falls short is against ambiguous behaviour such as a hug or losing track of a subject in the frame. The resulting model has potential for deployment within an airport if improvements are made to cope with the vast number of potential passengers in view as well as training against further ambiguous behaviours which will arise in an airport setting. In turn, will provide the capability to enhance security surveillance and improve airport safety.

Graph and Recurrent Neural Network-based Vehicle Trajectory Prediction For Highway Driving

2021-09-19
Xiaoyu Mo , Yang Xing , Chen Lv
Integrating trajectory prediction to the decision-making and planning modules of modular autonomous driving systems is expected to improve the safety and efficiency of self-driving vehicles. However, a vehicle's future trajectory … Integrating trajectory prediction to the decision-making and planning modules of modular autonomous driving systems is expected to improve the safety and efficiency of self-driving vehicles. However, a vehicle's future trajectory prediction is a challenging task since it is affected by the social interactive behaviors of neighboring vehicles, and the number of neighboring vehicles can vary in different situations. This work proposes a GNN-RNN based Encoder-Decoder network for interaction-aware trajectory prediction, where vehicles' dynamics features are extracted from their historical tracks using RNN, and the inter-vehicular interaction is represented by a directed graph and encoded using a GNN. The parallelism of GNN implies the proposed method's potential to predict multi-vehicular trajectories simultaneously. Evaluation on the dataset extracted from the NGSIM US-101 dataset shows that the proposed model is able to predict a target vehicle's trajectory in situations with a variable number of surrounding vehicles.
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Decision Making of Connected Automated Vehicles at an Unsignalized Roundabout Considering Personalized Driving Behaviours

2021-04-14
Peng Hang , Chao Huang , Zhongxu Hu +2 more
To improve the safety and efficiency of the intelligent transportation system, particularly in complex urban scenarios, in this paper a game theoretic decision-making framework is designed for connected automated vehicles … To improve the safety and efficiency of the intelligent transportation system, particularly in complex urban scenarios, in this paper a game theoretic decision-making framework is designed for connected automated vehicles (CAVs) at unsignalized roundabouts considering their personalized driving behaviours. Within the decision-making framework, a motion prediction module is designed and optimized using model predictive control (MPC) to enhance the effectiveness and accuracy of the decision-making algorithm. Besides, the payoff function of decision making is defined with the consideration of vehicle safety, ride comfort and travel efficiency. Additionally, the constraints of the decision-making problem are constructed. Based on the established decision-making model, Stackelberg game and grand coalition game approaches are adopted to address the decision making of CAVs at an unsignalized roundabout. Three testing cases considering personalized driving behaviours are carried out to verify the performance of the developed decision-making algorithms. The testing results show that the proposed game theoretic decision-making framework is able to make safe and reasonable decisions for CAVs in the complex urban scenarios, validating its feasibility and effectiveness. Stackelberg game approach shows its advantage in guaranteeing personalized driving objectives of individuals, while the grand coalition game approach is advantageous regarding the efficiency improvement of the transportation system.
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Cooperative Decision Making of Connected Automated Vehicles at Multi-Lane Merging Zone: A Coalitional Game Approach

2021-04-02
Peng Hang , Chen Lv , Chao Huang +2 more
To address the safety and efficiency issues of vehicles at multi-lane merging zones, a cooperative decision-making framework is designed for connected automated vehicles (CAVs) using a coalitional game approach. Firstly, … To address the safety and efficiency issues of vehicles at multi-lane merging zones, a cooperative decision-making framework is designed for connected automated vehicles (CAVs) using a coalitional game approach. Firstly, a motion prediction module is established based on the simplified single-track vehicle model for enhancing the accuracy and reliability of the decision-making algorithm. Then, the cost function and constraints of the decision making are designed considering multiple performance indexes, i.e. the safety, comfort and efficiency. Besides, in order to realize human-like and personalized smart mobility, different driving characteristics are considered and embedded in the modeling process. Furthermore, four typical coalition models are defined for CAVS at the scenario of a multi-lane merging zone. Then, the coalitional game approach is formulated with model predictive control (MPC) to deal with decision making of CAVs at the defined scenario. Finally, testings are carried out in two cases considering different driving characteristics to evaluate the performance of the developed approach. The testing results show that the proposed coalitional game based method is able to make reasonable decisions and adapt to different driving characteristics for CAVs at the multi-lane merging zone. It guarantees the safety and efficiency of CAVs at the complex dynamic traffic condition, and simultaneously accommodates the objectives of individual vehicles, demonstrating the feasibility and effectiveness of the proposed approach.
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Deep convolutional neural network-based Bernoulli heatmap for head pose estimation

2021-01-19
Zhongxu Hu , Yang Xing , Chen Lv +2 more
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Human-Machine Adaptive Shared Control for Safe Automated Driving under Automation Degradation

2021-01-01
Chao Huang , Chen Lv , Peng Hang +2 more
In this paper, a human-machine adaptive shared control method is proposed for automated vehicles (AVs) under automation performance degradation. First, a novel risk assessment module is proposed to monitor driving … In this paper, a human-machine adaptive shared control method is proposed for automated vehicles (AVs) under automation performance degradation. First, a novel risk assessment module is proposed to monitor driving behavior and evaluate automation performance degradation for AVs. Then, an adaptive control authority allocation module is developed. In the event of any performance degradation detection, the allocated control authority of the automation system is decreased based on the assessed risk to reduce the potential risk of vehicle motion. Consequently, the control authority allocated to the human driver is adaptively increased and thus requires more driver engagement in the control loop to compensate for the automation degradation and ensure AV safety. Experimental validation is conducted under different driving scenarios. The testing results show that the proposed approach is able to effectively compensate for the performance degradation of vehicle automation through the human-machine adaptive shared control, ensuring the safety of automated driving

Cooperative Decision Making of Connected Automated Vehicles at Multi-lane Merging Zone: A Coalitional Game Approach

2021-01-01
Peng Hang , Chen Lv , Chao Huang +2 more
To address the safety and efficiency issues of vehicles at multi-lane merging zones, a cooperative decision-making framework is designed for connected automated vehicles (CAVs) using a coalitional game approach. Firstly, … To address the safety and efficiency issues of vehicles at multi-lane merging zones, a cooperative decision-making framework is designed for connected automated vehicles (CAVs) using a coalitional game approach. Firstly, a motion prediction module is established based on the simplified single-track vehicle model for enhancing the accuracy and reliability of the decision-making algorithm. Then, the cost function and constraints of the decision making are designed considering multiple performance indexes, i.e. the safety, comfort and efficiency. Besides, in order to realize human-like and personalized smart mobility, different driving characteristics are considered and embedded in the modeling process. Furthermore, four typical coalition models are defined for CAVS at the scenario of a multi-lane merging zone. Then, the coalitional game approach is formulated with model predictive control (MPC) to deal with decision making of CAVs at the defined scenario. Finally, testings are carried out in two cases considering different driving characteristics to evaluate the performance of the developed approach. The testing results show that the proposed coalitional game based method is able to make reasonable decisions and adapt to different driving characteristics for CAVs at the multi-lane merging zone. It guarantees the safety and efficiency of CAVs at the complex dynamic traffic condition, and simultaneously accommodates the objectives of individual vehicles, demonstrating the feasibility and effectiveness of the proposed approach.

Decision Making of Connected Automated Vehicles at An Unsignalized Roundabout Considering Personalized Driving Behaviours

2021-01-01
Peng Hang , Chao Huang , Zhongxu Hu +1 more
To improve the safety and efficiency of the intelligent transportation system, particularly in complex urban scenarios, in this paper a game theoretic decision-making framework is designed for connected automated vehicles … To improve the safety and efficiency of the intelligent transportation system, particularly in complex urban scenarios, in this paper a game theoretic decision-making framework is designed for connected automated vehicles (CAVs) at unsignalized roundabouts considering their personalized driving behaviours. Within the decision-making framework, a motion prediction module is designed and optimized using model predictive control (MPC) to enhance the effectiveness and accuracy of the decision-making algorithm. Besides, the payoff function of decision making is defined with the consideration of vehicle safety, ride comfort and travel efficiency. Additionally, the constraints of the decision-making problem are constructed. Based on the established decision-making model, Stackelberg game and grand coalition game approaches are adopted to address the decision making of CAVs at an unsignalized roundabout. Three testing cases considering personalized driving behaviours are carried out to verify the performance of the developed decision-making algorithms. The testing results show that the proposed game theoretic decision-making framework is able to make safe and reasonable decisions for CAVs in the complex urban scenarios, validating its feasibility and effectiveness. Stackelberg game approach shows its advantage in guaranteeing personalized driving objectives of individuals, while the grand coalition game approach is advantageous regarding the efficiency improvement of the transportation system.
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Human-in-the-Loop Deep Reinforcement Learning with Application to Autonomous Driving

2021-01-01
Jingda Wu , Zhiyu Huang , Chao Huang +4 more
Due to the limited smartness and abilities of machine intelligence, currently autonomous vehicles are still unable to handle all kinds of situations and completely replace drivers. Because humans exhibit strong … Due to the limited smartness and abilities of machine intelligence, currently autonomous vehicles are still unable to handle all kinds of situations and completely replace drivers. Because humans exhibit strong robustness and adaptability in complex driving scenarios, it is of great importance to introduce humans into the training loop of artificial intelligence, leveraging human intelligence to further advance machine learning algorithms. In this study, a real-time human-guidance-based deep reinforcement learning (Hug-DRL) method is developed for policy training of autonomous driving. Leveraging a newly designed control transfer mechanism between human and automation, human is able to intervene and correct the agent's unreasonable actions in real time when necessary during the model training process. Based on this human-in-the-loop guidance mechanism, an improved actor-critic architecture with modified policy and value networks is developed. The fast convergence of the proposed Hug-DRL allows real-time human guidance actions to be fused into the agent's training loop, further improving the efficiency and performance of deep reinforcement learning. The developed method is validated by human-in-the-loop experiments with 40 subjects and compared with other state-of-the-art learning approaches. The results suggest that the proposed method can effectively enhance the training efficiency and performance of the deep reinforcement learning algorithm under human guidance, without imposing specific requirements on participant expertise and experience.

Heterogeneous Edge-Enhanced Graph Attention Network For Multi-Agent Trajectory Prediction

2021-01-01
Xiaoyu Mo , Yang Xing , Chen Lv
Simultaneous trajectory prediction for multiple heterogeneous traffic participants is essential for the safe and efficient operation of connected automated vehicles under complex driving situations in the real world. The multi-agent … Simultaneous trajectory prediction for multiple heterogeneous traffic participants is essential for the safe and efficient operation of connected automated vehicles under complex driving situations in the real world. The multi-agent prediction task is challenging, as the motions of traffic participants are affected by many factors, including their individual dynamics, their interactions with surrounding agents, the traffic infrastructures, and the number and modalities of the target agents. To further advance the trajectory prediction techniques, in this work we propose a three-channel framework together with a novel Heterogeneous Edge-enhanced graph ATtention network (HEAT), which is able to deal with the heterogeneity of the target agents and traffic participants involved. Specifically, the agent's dynamics are extracted from their historical states using type-specific encoders. The inter-agent interactions are represented with a directed edge-featured heterogeneous graph, and then interaction features are extracted using the proposed HEAT network. Besides, the map features are shared across all agents by introducing a selective gate mechanism. And finally, the trajectories of multi-agent are executed simultaneously. Validations using both urban and highway driving datasets show that the proposed model can realize simultaneous trajectory predictions for multiple agents under complex traffic situations, and achieve state-of-the-art performance with respect to prediction accuracy, demonstrating its feasibility and effectiveness.
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Graph and Recurrent Neural Network-based Vehicle Trajectory Prediction For Highway Driving

2021-01-01
Xiaoyu Mo , Yang Xing , Chen Lv
Integrating trajectory prediction to the decision-making and planning modules of modular autonomous driving systems is expected to improve the safety and efficiency of self-driving vehicles. However, a vehicle's future trajectory … Integrating trajectory prediction to the decision-making and planning modules of modular autonomous driving systems is expected to improve the safety and efficiency of self-driving vehicles. However, a vehicle's future trajectory prediction is a challenging task since it is affected by the social interactive behaviors of neighboring vehicles, and the number of neighboring vehicles can vary in different situations. This work proposes a GNN-RNN based Encoder-Decoder network for interaction-aware trajectory prediction, where vehicles' dynamics features are extracted from their historical tracks using RNN, and the inter-vehicular interaction is represented by a directed graph and encoded using a GNN. The parallelism of GNN implies the proposed method's potential to predict multi-vehicular trajectories simultaneously. Evaluation on the dataset extracted from the NGSIM US-101 dataset shows that the proposed model is able to predict a target vehicle's trajectory in situations with a variable number of surrounding vehicles.
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An Integrated Framework of Decision Making and Motion Planning for Autonomous Vehicles Considering Social Behaviors

2020-11-25
Peng Hang , Chen Lv , Chao Huang +3 more
This paper presents a novel integrated approach to deal with the decision making and motion planning for lane-change maneuvers of autonomous vehicle (AV) considering social behaviors of surrounding traffic occupants. … This paper presents a novel integrated approach to deal with the decision making and motion planning for lane-change maneuvers of autonomous vehicle (AV) considering social behaviors of surrounding traffic occupants. Reflected by driving styles and intentions of surrounding vehicles, the social behaviors are taken into consideration during the modelling process. Then, the Stackelberg Game theory is applied to solve the decision-making, which is formulated as a non-cooperative game problem. Besides, potential field is adopted in the motion planning model, which uses different potential functions to describe surrounding vehicles with different behaviors and road constraints. Then, Model Predictive Control (MPC) is utilized to predict the state and trajectory of the autonomous vehicle. Finally, the decision-making and motion planning is then integrated into a constrained multi-objective optimization problem. Three testing scenarios considering different social behaviors of surrounding vehicles are carried out to validate the performance of the proposed approach. Testing results show that the integrated approach is able to address different social interactions with other traffic participants, and make proper and safe decisions and planning for autonomous vehicles, demonstrating its feasibility and effectiveness.
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Human-Like Decision Making for Autonomous Driving: A Noncooperative Game Theoretic Approach

2020-11-17
Peng Hang , Chen Lv , Yang Xing +2 more
Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers' traffic ecology and minimize … Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers' traffic ecology and minimize the effect of AVs and their misfit with human drivers, are issues worthy of consideration. Moreover, different passengers have different needs for AVs, thus, how to provide personalized choices for different passengers is another issue for AVs. Therefore, a human-like decision making framework is designed for AVs in this paper. Different driving styles and social interaction characteristics are formulated for AVs regarding driving safety, ride comfort and travel efficiency, which are considered in the modeling process of decision making. Then, Nash equilibrium and Stackelberg game theory are applied to the noncooperative decision making. In addition, potential field method and model predictive control (MPC) are combined to deal with the motion prediction and planning for AVs, which provides predicted motion information for the decision-making module. Finally, two typical testing scenarios of lane change, i.e., merging and overtaking, are carried out to evaluate the feasibility and effectiveness of the proposed decision-making framework considering different human-like behaviors. Testing results indicate that both the two game theoretic approaches can provide reasonable human-like decision making for AVs. Compared with the Nash equilibrium approach, under the normal driving style, the cost value of decision making using the Stackelberg game theoretic approach is reduced by over 20%.
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Interaction-Aware Trajectory Prediction of Connected Vehicles using CNN-LSTM Networks

2020-10-18
Xiaoyu Mo , Yang Xing , Chen Lv
Predicting the future trajectory of a surrounding vehicle in congested traffic is one of the necessary abilities of an autonomous vehicle. In congestion, a vehicle's future movement is the result … Predicting the future trajectory of a surrounding vehicle in congested traffic is one of the necessary abilities of an autonomous vehicle. In congestion, a vehicle's future movement is the result of its interaction with surrounding vehicles. A vehicle in congestion may have many neighbors in a relatively short distance, while only a small part of neighbors affect its future trajectory mostly. In this work, An interaction-aware method that predicts the future trajectory of an ego vehicle considering its interaction with eight surrounding vehicles is proposed. The dynamics of vehicles are encoded by LSTMs with shared weights, and the interaction is extracted with a simple CNN. The proposed model is trained and tested on trajectories extracted from the publicly accessible NGSIM US-101 dataset. Quantitative experimental results show that the proposed model outperforms previous models in root-mean-square error (RMSE). Results visualization shows that the model is able to predict future trajectory induced by lane change before the vehicle operates noticeable lateral movement to initiate lane changing.
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Decision-making in driver-automation shared control: A review and perspectives

2020-07-24
Wenshuo Wang , Xiaoxiang Na , Dongpu Cao +4 more
Shared control schemes allow a human driver to work with an automated driving agent in driver-vehicle systems while retaining the driver's abilities to control. The human driver, as an essential … Shared control schemes allow a human driver to work with an automated driving agent in driver-vehicle systems while retaining the driver's abilities to control. The human driver, as an essential agent in the driver-vehicle shared control systems, should be precisely modeled regarding their cognitive processes, control strategies, and decision-making processes. The interactive strategy design between drivers and automated driving agents brings an excellent challenge for human-centric driver assistance systems due to the inherent characteristics of humans. Many open-ended questions arise, such as what proper role of human drivers should act in a shared control scheme? How to make an intelligent decision capable of balancing the benefits of agents in shared control systems? Due to the advent of these attentions and questions, it is desirable to present a survey on the decision-making between human drivers and highly automated vehicles, to understand their architectures, human driver modeling, and interaction strategies under the driver-vehicle shared schemes. Finally, we give a further discussion on the key future challenges and opportunities. They are likely to shape new potential research directions.
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Multi-Modal Sensor Fusion-Based Deep Neural Network for End-to-End Autonomous Driving With Scene Understanding

2020-06-17
Zhiyu Huang , Chen Lv , Yang Xing +1 more
This study aims to improve the performance and generalization capability of end-to-end autonomous driving with scene understanding leveraging deep learning and multimodal sensor fusion techniques. The designed end-to-end deep neural … This study aims to improve the performance and generalization capability of end-to-end autonomous driving with scene understanding leveraging deep learning and multimodal sensor fusion techniques. The designed end-to-end deep neural network takes as input the visual image and associated depth information in an early fusion level and outputs the pixel-wise semantic segmentation as scene understanding and vehicle control commands concurrently. The end-to-end deep learning-based autonomous driving model is tested in high-fidelity simulated urban driving conditions and compared with the benchmark of CoRL2017 and NoCrash. The testing results show that the proposed approach is of better performance and generalization ability, achieving a 100% success rate in static navigation tasks in both training and unobserved situations, as well as better success rates in other tasks than the prior models. A further ablation study shows that the model with the removal of multimodal sensor fusion or scene understanding pales in the new environment because of the false perception. The results verify that the performance of our model is improved by the synergy of multimodal sensor fusion with scene understanding subtask, demonstrating the feasibility and effectiveness of the developed deep neural network with multimodal sensor fusion.
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Human-Machine Collaboration for Automated Vehicles via an Intelligent Two-Phase Haptic Interface

2020-01-01
Chen Lv , Yutong Li , Yang Xing +4 more
Prior to realizing fully autonomous driving, human intervention will be required periodically to guarantee vehicle safety. This fact poses a new challenge in human-machine interaction, particularly during control authority transition … Prior to realizing fully autonomous driving, human intervention will be required periodically to guarantee vehicle safety. This fact poses a new challenge in human-machine interaction, particularly during control authority transition from the automated functionality to a human driver. This paper addresses this challenge by proposing an intelligent haptic interface based on a newly developed two-phase human-machine interaction model. The intelligent haptic torque is applied on the steering wheel and switches its functionality between predictive guidance and haptic assistance according to the varying state and control ability of human drivers, helping drivers gradually resume manual control during takeover. The developed approach is validated by conducting vehicle experiments with 26 human participants. The results suggest that the proposed method can effectively enhance the driving state recovery and control performance of human drivers during takeover compared with an existing approach, further improving the safety and smoothness of the human-machine interaction in automated vehicles.
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A Unified Multi-scale and Multi-task Learning Framework for Driver Behaviors Reasoning

2020-01-01
Yang Xing , Chen Lv , Dongpu Cao +1 more
Mutual understanding between driver and vehicle is critically important to the design of intelligent vehicles and customized interaction interface. In this study, a unified driver behavior reasoning system toward multi-scale … Mutual understanding between driver and vehicle is critically important to the design of intelligent vehicles and customized interaction interface. In this study, a unified driver behavior reasoning system toward multi-scale and multi-tasks behavior recognition is proposed. Specifically, a multi-scale driver behavior recognition system is designed to recognize both the driver's physical and mental states based on a deep encoder-decoder framework. This system can jointly recognize three driver behaviors with different time scales based on the shared encoder network. Driver body postures and mental behaviors include intention and emotion are studied and identified. The encoder network is designed based on a deep convolutional neural network (CNN), and several decoders for different driver states estimation are proposed with fully connected (FC) and long short-term memory (LSTM) based recurrent neural networks (RNN). The joint feature learning with the CNN encoder increases the computational efficiency and feature diversity, while the customized decoders enable an efficient multi-tasks inference. The proposed framework can be used as a solution to exploit the relationship between different driver states, and it is found that when drivers generate lane change intentions, their emotions usually keep neutral state and more focus on the task. Two naturalistic datasets are used to investigate the model performance, which is a local highway dataset, namely, CranData and one public dataset from Brain4Cars. The testing results on these two datasets show accurate performance and outperform existing methods on driver postures, intention, and emotion recognition.

Human-Like Decision Making for Autonomous Driving: A Noncooperative Game Theoretic Approach

2020-01-01
Peng Hang , Chen Lv , Yang Xing +2 more
Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers traffic ecology and minimize … Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers traffic ecology and minimize the effect of AVs and their misfit with human drivers, are issues worthy of consideration. Moreover, different passengers have different needs for AVs, thus, how to provide personalized choices for different passengers is another issue for AVs. Therefore, a human-like decision making framework is designed for AVs in this paper. Different driving styles and social interaction characteristics are formulated for AVs regarding driving safety, ride comfort and travel efficiency, which are considered in the modeling process of decision making. Then, Nash equilibrium and Stackelberg game theory are applied to the noncooperative decision making. In addition, potential field method and model predictive control (MPC) are combined to deal with the motion prediction and planning for AVs, which provides predicted motion information for the decision-making module. Finally, two typical testing scenarios of lane change, i.e., merging and overtaking, are carried out to evaluate the feasibility and effectiveness of the proposed decision-making framework considering different human-like behaviors. Testing results indicate that both the two game theoretic approaches can provide reasonable human-like decision making for AVs. Compared with the Nash equilibrium approach, under the normal driving style, the cost value of decision making using the Stackelberg game theoretic approach is reduced by over 20%.
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Interaction-Aware Trajectory Prediction of Connected Vehicles using CNN-LSTM Networks

2020-01-01
Xiaoyu Mo , Yang Xing
Predicting the future trajectory of a surrounding vehicle in congested traffic is one of the basic abilities of an autonomous vehicle. In congestion, a vehicle's future movement is the result … Predicting the future trajectory of a surrounding vehicle in congested traffic is one of the basic abilities of an autonomous vehicle. In congestion, a vehicle's future movement is the result of its interaction with surrounding vehicles. A vehicle in congestion may have many neighbors in a relatively short distance, while only a small part of neighbors affect its future trajectory mostly. In this work, An interaction-aware method which predicts the future trajectory of an ego vehicle considering its interaction with eight surrounding vehicles is proposed. The dynamics of vehicles are encoded by LSTMs with shared weights, and the interaction is extracted with a simple CNN. The proposed model is trained and tested on trajectories extracted from the publicly accessible NGSIM US-101 dataset. Quantitative experimental results show that the proposed model outperforms previous models in terms of root-mean-square error (RMSE). Results visualization shows that the model is able to predict future trajectory induced by lane change before the vehicle operate obvious lateral movement to initiate lane changing.

Deep Convolutional Neural Network-based Bernoulli Heatmap for Head Pose Estimation

2020-01-01
Zhongxu Hu , Yang Xing , Chen Lv +2 more
Head pose estimation is a crucial problem for many tasks, such as driver attention, fatigue detection, and human behaviour analysis. It is well known that neural networks are better at … Head pose estimation is a crucial problem for many tasks, such as driver attention, fatigue detection, and human behaviour analysis. It is well known that neural networks are better at handling classification problems than regression problems. It is an extremely nonlinear process to let the network output the angle value directly for optimization learning, and the weight constraint of the loss function will be relatively weak. This paper proposes a novel Bernoulli heatmap for head pose estimation from a single RGB image. Our method can achieve the positioning of the head area while estimating the angles of the head. The Bernoulli heatmap makes it possible to construct fully convolutional neural networks without fully connected layers and provides a new idea for the output form of head pose estimation. A deep convolutional neural network (CNN) structure with multiscale representations is adopted to maintain high-resolution information and low-resolution information in parallel. This kind of structure can maintain rich, high-resolution representations. In addition, channelwise fusion is adopted to make the fusion weights learnable instead of simple addition with equal weights. As a result, the estimation is spatially more precise and potentially more accurate. The effectiveness of the proposed method is empirically demonstrated by comparing it with other state-of-the-art methods on public datasets.
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Driving Conditions-Driven Energy Management for Hybrid Electric Vehicles: A Review

2020-01-01
Teng Liu , Xiaolin Tang , Jinwei Zhang +3 more
Motivated by the concerns on transported fuel consumption and global air pollution, industrial engineers, and academic researchers have made many efforts to construct more efficient and environment-friendly vehicles. Hybrid electric … Motivated by the concerns on transported fuel consumption and global air pollution, industrial engineers, and academic researchers have made many efforts to construct more efficient and environment-friendly vehicles. Hybrid electric vehicles (HEVs) are the representative ones because they can satisfy the power demand by coordinating energy supplements among different energy storage devices. To achieve this goal, energy management approaches are crucial technology, and driving cycles are the critical influence factor. Therefore, this paper aims to summarize driving cycle-driven energy management strategies (EMSs) for HEVs. First, the definition and significance of driving cycles in the energy management field are clarified, and the recent literature in this research domain is reviewed and revisited. In addition, according to the known information of driving cycles, the EMSs are divided into three categories, and the relevant study directions, such as standard driving cycles, long-term driving cycle generation (LT-DCG) and short-term driving cycle prediction (ST-DCP) are illuminated and analyzed. Furthermore, the existing database of driving cycles in highway and urban aspects are displayed and discussed. Finally, this article also elaborates on the future prospects of energy management technologies related to driving cycles. This paper focusing on helping the relevant researchers realize the state-of-the-art of HEVs energy management field and also recognize its future development direction.
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Defining Digital Quadruplets in the Cyber-Physical-Social Space for Parallel Driving

2020-01-01
Teng Liu , Yang Xing , Long Chen +2 more
Parallel driving is a novel framework to synthesize vehicle intelligence and transport automation. This article aims to define digital quadruplets in parallel driving. In the cyber-physical-social systems (CPSS), based on … Parallel driving is a novel framework to synthesize vehicle intelligence and transport automation. This article aims to define digital quadruplets in parallel driving. In the cyber-physical-social systems (CPSS), based on the ACP method, the names of the digital quadruplets are first given, which are descriptive, predictive, prescriptive and real vehicles. The objectives of the three virtual digital vehicles are interacting, guiding, simulating and improving with the real vehicles. Then, the three virtual components of the digital quadruplets are introduced in detail and their applications are also illustrated. Finally, the real vehicles in the parallel driving system and the research process of the digital quadruplets are depicted. The presented digital quadruplets in parallel driving are expected to make the future connected automated driving safety, efficiently and synergistically.

ReCoG: A Deep Learning Framework with Heterogeneous Graph for Interaction-Aware Trajectory Prediction

2020-01-01
Xiaoyu Mo , Yang Xing , Chen Lv
Predicting the future trajectory of surrounding vehicles is essential for the navigation of autonomous vehicles in complex real-world driving scenarios. It is challenging as a vehicle's motion is affected by … Predicting the future trajectory of surrounding vehicles is essential for the navigation of autonomous vehicles in complex real-world driving scenarios. It is challenging as a vehicle's motion is affected by many factors, including its surrounding infrastructures and vehicles. In this work, we develop the ReCoG (Recurrent Convolutional and Graph Neural Networks), which is a general scheme that represents vehicle interactions with infrastructure information as a heterogeneous graph and applies graph neural networks (GNNs) to model the high-level interactions for trajectory prediction. Nodes in the graph contain corresponding features, where a vehicle node contains its sequential feature encoded using Recurrent Neural Network (RNN), and an infrastructure node contains spatial feature encoded using Convolutional Neural Network (CNN). Then the ReCoG predicts the future trajectory of the target vehicle by jointly considering all of the features. Experiments are conducted by using the INTERACTION dataset. Experimental results show that the proposed ReCoG outperforms other state-of-the-art methods in terms of different types of displacement error, validating the feasibility and effectiveness of the developed approach.

A Universal Prior Distribution for Bayesian Consistency of Non parametric Procedures

2015-03-04
Yang Xing
The introduction of the Hausdorff α-entropy in Xing (2008a Xing, Y. (2008a). Convergence rates of posterior distributions for observations without the iid structure, 38 pages. Available at: www.arxiv.org:0811.4677v1. [Google Scholar]), … The introduction of the Hausdorff α-entropy in Xing (2008a Xing, Y. (2008a). Convergence rates of posterior distributions for observations without the iid structure, 38 pages. Available at: www.arxiv.org:0811.4677v1. [Google Scholar]), Xing (2008b Xing, Y. (2008b). On adaptive Bayesian inference. Electron. J. Stat. 2:848–862.[Crossref] , [Google Scholar]), Xing (2010 Xing, Y. (2010). Rates of posterior convergence for iid Observations. Commun. Stat. Theory Methods. 39(19):3389–3398.[Taylor & Francis Online] , [Google Scholar]), Xing (2011 Xing, Y. (2011). Convergence rates of nonparametric posterior distributions. J. Stat. Plann. Inference 141:3382–3390.[Crossref], [Web of Science ®] , [Google Scholar]), and Xing and Ranneby (2009 Xing, Y., Ranneby, B. (2009). Sufficient conditions for Bayesian consistency. J. Stat. Plann. Inference. 139:2479–2489.[Crossref], [Web of Science ®] , [Google Scholar]) has lead a series of improvements of well-known results on posterior consistency. In this paper we discuss an application of the Hausdorff α-entropy. We construct a universal prior distribution such that the corresponding posterior distribution is almost surely consistent. The approach of the construction of this type of prior distribution is natural, but it works very well for all separable models. We illustrate such prior distributions by examples. In particular, we obtain that if the true density function is known to be some normal probability density function with unknown mean and unknown variance then without any additional assumption one can construct a prior distribution which leads to posterior consistency.

On strong Hellinger consistency of posterior distributions

2012-02-02
Yang Xing , Bo Ranneby
Abstract We establish a sufficient condition ensuring strong Hellinger consistency of posterior distributions. We also prove a strong Hellinger consistency theorem for the pseudoposterior distributions based on the likelihood ratio … Abstract We establish a sufficient condition ensuring strong Hellinger consistency of posterior distributions. We also prove a strong Hellinger consistency theorem for the pseudoposterior distributions based on the likelihood ratio with power 0<α<1, which are introduced by Walker and Hjort [2001 ‘On Bayesian Consistency’, J. R. Statist. Soc., B 63, 811–821]. Our result is an extension of their theorem for α=½. Keywords: Hellinger consistencyposterior distributionnonparametric model AMS 2000 Subject Classifications:: 62G0762G2062F15 Acknowledgements We are grateful to an associate editor and two anonymous referees for their helpful comments and suggestions.

Convergence rates of nonparametric posterior distributions

2010-10-29
Yang Xing
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Rates of Posterior Convergence for iid Observations

2010-09-12
Yang Xing
By means of the Hausdorff α-entropy introduced by Xing and Ranneby (2009 Xing , Y. , Ranneby , B. ( 2009 ). Sufficient conditions for Bayesian consistency . J. Statist. … By means of the Hausdorff α-entropy introduced by Xing and Ranneby (2009 Xing , Y. , Ranneby , B. ( 2009 ). Sufficient conditions for Bayesian consistency . J. Statist. Plann. Inference. 139 : 2479 – 2489 .[Crossref] , [Google Scholar]), we give two theorems on rates of in-probability convergence of posterior distributions. The result is applied in study of the Bernstein polynomial priors.

The General Definition of the Complex Monge–Ampère Operator on Compact Kähler Manifolds

2009-12-22
Yang Xing
Abstract We introduce a wide subclass of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well defined and the convergence theorem is valid. We … Abstract We introduce a wide subclass of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well defined and the convergence theorem is valid. We also prove that is a convex cone and includes all quasi-plurisubharmonic functions that are in the Cegrell class.
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Asymptotic behavior of Bayesian nonparametric procedures

2009-01-01
Yang Xing
Asymptotics plays a crucial role in statistics. The theory of asymptotic consistency of Bayesian nonparametric procedures has been developed by many authors, including Schwartz (1965), Barron, Schervish and Wasserman (1999), … Asymptotics plays a crucial role in statistics. The theory of asymptotic consistency of Bayesian nonparametric procedures has been developed by many authors, including Schwartz (1965), Barron, Schervish and Wasserman (1999), Ghosal, Ghosh and Ramamoorthi (1999), Ghosal, Ghosh and van der Vaart (2000), Shen and Wasserman (2001), Walker and Hjort (2001), Walker (2004), Ghosal and van der Vaart (2007) and Walker, Lijoi and Prunster (2007). This theory is mainly based on existence of uniformly exponentially consistent tests, computation of a metric entropy and measure of a prior concentration around the true value of parameter. However, both the test condition and the metric entropy condition depend on models but not on prior distributions. Because a posterior distribution depends on the complexity of the model only through its prior distribution, it is therefore natural to explore appropriate conditions which incorporate prior distributions. In this thesis we introduce the Hausdorff entropy and an integration condition, both of which incorporate prior distributions and moreover are weaker than the metric entropy condition and the test condition, respectively. Furthermore, we provide an improved method to measure the prior concentration. By means of these new quantities, we derive several types of general posterior consistency theorems and general posterior convergence rate theorems for i.i.d. and non-i.i.d. models, which lead to improvements in a number of currently known theorems and their applications. We also study rate adaptation for density estimation within the Bayesian framework and particularly obtain that the Bayesian procedure with hierarchical prior distributions for log spline densities and a finite number of models achieves the optimal minimax rate when the true density is HA¶lder-continuous. This result disconfirms a conjecture given by Ghosal, Lember and van der Vaart (2003). Finally, we find a new both necessary and sufficient condition on Bayesian exponential consistency for prior distributions with the Kullback-Leibler support property.

Sufficient conditions for Bayesian consistency

2008-12-01
Yang Xing , Bo Ranneby

A strong comparison principle of plurisubharmonic functions with finite pluricomplex energy

2008-12-01
Yang Xing
A strong comparison principle of plurisubharmonic functions with finite pluricomplex energy A strong comparison principle of plurisubharmonic functions with finite pluricomplex energy
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Continuity of the Complex Monge–Ampère operator on compact Kähler manifolds

2008-09-02
Yang Xing
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Both necessary and sufficient conditions for Bayesian exponential consistency

2008-01-01
Yang Xing , Bo Ranneby
The last decade has seen a remarkable development in the theory of asymptotics of Bayesian nonparametric procedures. Exponential consistency has played an important role in this area. It is known … The last decade has seen a remarkable development in the theory of asymptotics of Bayesian nonparametric procedures. Exponential consistency has played an important role in this area. It is known that the condition of $f_0$ being in the Kullback-Leibler support of the prior cannot ensure exponential consistency of posteriors. Many authors have obtained additional sufficient conditions for exponential consistency of posteriors, see, for instance, Schwartz (1965), Barron, Schervish and Wasserman (1999), Ghosal, Ghosh and Ramamoorthi (1999), Walker (2004), Xing and Ranneby (2008). However, given the Kullback-Leibler support condition, less is known about both necessary and sufficient conditions. In this paper we give one type of both necessary and sufficient conditions. As a consequence we derive a simple sufficient condition on Bayesian exponential consistency, which is weaker than the previous sufficient conditions.

Convergence in Capacity

2008-01-01
Yang Xing
We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures … We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures which is essentially equivalent to convergence in the capacity C n of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity C n-1 of functions in some case. As applications we give certain stability theorems of solutions of Monge-Ampère equations.
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Convergence rates of posterior distributions for observations without the iid structure

2008-01-01
Yang Xing
The classical condition on the existence of uniformly exponentially consistent tests for testing the true density against the complement of its arbitrary neighborhood has been widely adopted in study of … The classical condition on the existence of uniformly exponentially consistent tests for testing the true density against the complement of its arbitrary neighborhood has been widely adopted in study of asymptotics of Bayesian nonparametric procedures. Because we follow a Bayesian approach, it seems to be more natural to explore alternative and appropriate conditions which incorporate the prior distribution. In this paper we supply a new prior-dependent integration condition to establish general posterior convergence rate theorems for observations which may not be independent and identically distributed. The posterior convergence rates for such observations have recently studied by Ghosal and van der Vaart \cite{ghv1}. We moreover adopt the Hausdorff $α$-entropy given by Xing and Ranneby \cite{xir1}\cite{xi1}, which is also prior-dependent and smaller than the widely used metric entropies. These lead to extensions of several existing theorems. In particular, we establish a posterior convergence rate theorem for general Markov processes and as its application we improve on the currently known posterior rate of convergence for a nonlinear autoregressive model.

Operation of fermat's last theorem

2008-01-01
Yang Xing
Pierre de Fermat first mentioned this world-known theorem.It will be perfect if we find out the clever operation.This study managed to work out the ingenious operation from the specific to … Pierre de Fermat first mentioned this world-known theorem.It will be perfect if we find out the clever operation.This study managed to work out the ingenious operation from the specific to general methods by using elementary mathematics knowledge.The equation xn+yn=zn(n2)(The letters are all positive integer except especially mentioned) was proven by quadratic equation.when x=10a,z does not equal positive integer.From this,we can get the conclusion 1 adds the rational number n power of exponent and n root is the irrational number.So we get the very method in this way.
Coauthor Papers Together
Chen Lv 21
Zhongxu Hu 13
Chao Huang 12
Peng Hang 12
Xiaoyu Mo 7
Weisi Guo 6
Antonios Tsourdos 5
Dongpu Cao 5
Fei‐Yue Wang 4
Bo Ranneby 3
Long Chen 3
Nanning Zheng 2
Lina Bao 2
Dongpu Cao 2
Zhiyu Huang 2
Wei‐Liang Qian 2
Jinjie Wang 2
Jingda Wu 2
Xiaoxiang Na 2
Siyu Teng 2
Daxin Tian 2
Yuchen Li 2
Dan Wen 2
İrem Üstek 2
Iván López Torrecillas 2
Sofiane Abadou 2
Quentin Fever 2
Sandhya Rani Kasthuri 2
Teng Liu 2
Jie Liu 2
Jinjun Wang 2
Jiaming Jiang 2
Chong Ye 2
Jay Desai 2
Shuifa Shen 2
Li Li 2
Adolfo Perrusquía 1
Brendan Copp 1
Ruolin Liu 1
Jiacheng Cai 1
LI Tianyue 1
Ahmed Ali 1
Xiaolin Tang 1
Valentin Sonntag 1
Muhammed Mehmet Unal 1
Adeola Aderogba 1
Benjamin T. Fraser 1
Yifan Zhao 1
Ziyue Wang 1
Junqiang Xi 1

A new capacity for plurisubharmonic functions

1982-01-01
Eric Bedford , B. A. Taylor
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New approaches to Bayesian consistency

2004-10-01
Stephen G. Walker
We use martingales to study Bayesian consistency. We derive sufficient conditions for both Hellinger and Kullback–Leibler consistency, which do not rely on the use of a sieve. Alternative sufficient conditions … We use martingales to study Bayesian consistency. We derive sufficient conditions for both Hellinger and Kullback–Leibler consistency, which do not rely on the use of a sieve. Alternative sufficient conditions for Hellinger consistency are also found and demonstrated on examples.
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The consistency of posterior distributions in nonparametric problems

1999-04-01
Andrew R. Barron , Mark J. Schervish , L. H. Wasserman
We give conditions that guarantee that the posterior probability of every Hellinger neighborhood of the true distribution tends to 1 almost surely. The conditions are (1) a requirement that the … We give conditions that guarantee that the posterior probability of every Hellinger neighborhood of the true distribution tends to 1 almost surely. The conditions are (1) a requirement that the prior not put high mass near distributions with very rough densities and (2) a requirement that the prior put positive mass in Kullback-Leibler neighborhoods of the true distribution. The results are based on the idea of approximating the set of distributions with a finite-dimensional set of distributions with sufficiently small Hellinger bracketing metric entropy. We apply the results to some examples.
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On Bayes procedures

1965-01-01
Lorraine Schwartz
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Sufficient conditions for Bayesian consistency

2008-12-01
Yang Xing , Bo Ranneby

Rates of convergence of posterior distributions

2001-06-01
Xiaotong Shen , Larry Wasserman
We compute the rate at which the posterior distribution concentrates around the true parameter value. The spaces we work in are quite general and include in finite dimensional cases. The … We compute the rate at which the posterior distribution concentrates around the true parameter value. The spaces we work in are quite general and include in finite dimensional cases. The rates are driven by two quantities: the size of the space, as measured by bracketing entropy, and the degree to which the prior concentrates in a small ball around the true parameter. We consider two examples.
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Human-Like Decision Making for Autonomous Driving: A Noncooperative Game Theoretic Approach

2020-11-17
Peng Hang , Chen Lv , Yang Xing +2 more
Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers' traffic ecology and minimize … Considering that human-driven vehicles and autonomous vehicles (AVs) will coexist on roads in the future for a long time, how to merge AVs into human drivers' traffic ecology and minimize the effect of AVs and their misfit with human drivers, are issues worthy of consideration. Moreover, different passengers have different needs for AVs, thus, how to provide personalized choices for different passengers is another issue for AVs. Therefore, a human-like decision making framework is designed for AVs in this paper. Different driving styles and social interaction characteristics are formulated for AVs regarding driving safety, ride comfort and travel efficiency, which are considered in the modeling process of decision making. Then, Nash equilibrium and Stackelberg game theory are applied to the noncooperative decision making. In addition, potential field method and model predictive control (MPC) are combined to deal with the motion prediction and planning for AVs, which provides predicted motion information for the decision-making module. Finally, two typical testing scenarios of lane change, i.e., merging and overtaking, are carried out to evaluate the feasibility and effectiveness of the proposed decision-making framework considering different human-like behaviors. Testing results indicate that both the two game theoretic approaches can provide reasonable human-like decision making for AVs. Compared with the Nash equilibrium approach, under the normal driving style, the cost value of decision making using the Stackelberg game theoretic approach is reduced by over 20%.
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Multi-Agent Tensor Fusion for Contextual Trajectory Prediction

2019-06-01
Tianyang Zhao , Yifei Xu , Mathew Monfort +5 more
Accurate prediction of others' trajectories is essential for autonomous driving. Trajectory prediction is challenging because it requires reasoning about agents' past movements, social interactions among varying numbers and kinds of … Accurate prediction of others' trajectories is essential for autonomous driving. Trajectory prediction is challenging because it requires reasoning about agents' past movements, social interactions among varying numbers and kinds of agents, constraints from the scene context, and the stochasticity of human behavior. Our approach models these interactions and constraints jointly within a novel Multi-Agent Tensor Fusion (MATF) network. Specifically, the model encodes multiple agents' past trajectories and the scene context into a Multi-Agent Tensor, then applies convolutional fusion to capture multiagent interactions while retaining the spatial structure of agents and the scene context. The model decodes recurrently to multiple agents' future trajectories, using adversarial loss to learn stochastic predictions. Experiments on both highway driving and pedestrian crowd datasets show that the model achieves state-of-the-art prediction accuracy.
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Convergence rates of posterior distributions

2000-04-01
Subhashis Ghosal , Jayanta K. Ghosh , Aad van der Vaart
We consider the asymptotic behavior of posterior distributions and Bayes estimators for infinite-dimensional statistical models. We give general results on the rate of convergence of the posterior measure. These are … We consider the asymptotic behavior of posterior distributions and Bayes estimators for infinite-dimensional statistical models. We give general results on the rate of convergence of the posterior measure. These are applied to several examples, including priors on finite sieves, log-spline models, Dirichlet processes and interval censoring.
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On the Asymptotic Behavior of Bayes Estimates in the Discrete Case II

1965-04-01
David A. Freedman
Doob (1949) obtained a very general result on the consistency of Bayes' estimates. Loosely, if any consistent estimates are available, then the Bayes' estimates are consistent for almost all values … Doob (1949) obtained a very general result on the consistency of Bayes' estimates. Loosely, if any consistent estimates are available, then the Bayes' estimates are consistent for almost all values of the parameter under the prior measure. If the parameter is thought of as being selected by nature through a random mechanism whose probability law is known, Doob's result is completely satisfactory. On the other hand, in some circumstances it is necessary to identify the exceptional null set. For example, if the parameter is thought of as fixed but unknown, and the prior measure is chosen as a convenient way to calculate estimates, it is important to know for which null set the method fails. In particular, it is desirable to choose the prior so that the null set is in fact empty. The problem is very delicate; considerable work [8], [9], [12] has been done on it recently, in quite general contexts and under severe regularity assumptions. It might therefore be of interest to discuss the simplest possible case, that of independent, identically distributed, discrete observations, in some detail. This will be done in Sections 3 and 4 when the observations take a finite set of possible values. Under this assumption, Section 3 shows that the posterior probability converges to point mass at the true parameter value among almost all sample sequences (for short, the posterior is consistent; see Definition 1) exactly for parameter values in the topological carrier of the prior. In Section 4, the asymptotic normality of the posterior is shown to follow from a local smoothness assumption about the prior. In both sections, results are obtained for priors which admit the possibility of an infinite number of states. The results of these sections are not entirely new; see pp. 333 ff. of [7], pp. 224 ff. of [10], [11]. They have not appeared in the literature, to the best of our knowledge, in a form as precise as Theorems 1, 3, 4. Theorem 2 is essentially the relevant special case of Theorem 7.4 of Schwartz (1961). In Sections 5 and 6, the case of a countable number of possible values is treated. We believe the results to be new. Here the general problem appears, because priors which assign positive mass near the true parameter value may lead to ridiculous estimates. The results of Section 3 (let alone 4) are false. In fact, Theorem 5 of Section 5 gives the following construction. Suppose that under the true parameter value the observations take an infinite number of values with positive probability. Then given any spurious (sub-)stochastic probability distribution, it is possible to find a prior assigning positive mass to any neighborhood of the true parameter value, but leading to a posterior probability which converges for almost all sample sequences to point mass at the spurious distribution. Indeed, there is a prior assigning positive mass to every open set of parameters, for which the posterior is consistent only at a set of parameters of the first category. To some extent, this happens because at any stage information about a finite number of stages only is available, but on the basis of this evidence, conclusions must be drawn about all states. If the prior measure has a serious prejudice about the shape of the tails, disaster ensues. In Section 6, it is shown that a simple condition on the prior measure (which serves to limit this prejudice) ensures the consistency of the posterior. Prior probabilities leading to posterior distributions consistent at all and asymptotically normal at essentially all (see Remark 3, Section 3) parameter values are constructed. Section 5 is independent of Sections 3 and 4; Section 6 is not. Section 6 overlaps to some extent with unpublished work of Kiefer and Wolfowitz; it has been extended in certain directions by Fabius (1963). The results of this paper were announced in [5]; some related work for continuous state space is described in [3]. It is a pleasure to thank two very helpful referees: whatever expository merit Section 5 has is due to them and to L. J. Savage.
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Convolutional Social Pooling for Vehicle Trajectory Prediction

2018-06-01
Nachiket Deo , Mohan M. Trivedi
Forecasting the motion of surrounding vehicles is a critical ability for an autonomous vehicle deployed in complex traffic. Motion of all vehicles in a scene is governed by the traffic … Forecasting the motion of surrounding vehicles is a critical ability for an autonomous vehicle deployed in complex traffic. Motion of all vehicles in a scene is governed by the traffic context, i.e., the motion and relative spatial configuration of neighboring vehicles. In this paper we propose an LSTM encoder-decoder model that uses convolutional social pooling as an improvement to social pooling layers for robustly learning interdependencies in vehicle motion. Additionally, our model outputs a multi-modal predictive distribution over future trajectories based on maneuver classes. We evaluate our model using the publicly available NGSIM US-101 and I-80 datasets. Our results show improvement over the state of the art in terms of RMS values of prediction error and negative log-likelihoods of true future trajectories under the model's predictive distribution. We also present a qualitative analysis of the model's predicted distributions for various traffic scenarios.
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PyTorch: An Imperative Style, High-Performance Deep Learning Library

2019-01-01
Adam Paszke , Sam Gross , Francisco Massa +7 more
Deep learning frameworks have often focused on either usability or speed, but not both. PyTorch is a machine learning library that shows that these two goals are in fact compatible: … Deep learning frameworks have often focused on either usability or speed, but not both. PyTorch is a machine learning library that shows that these two goals are in fact compatible: it was designed from first principles to support an imperative and Pythonic programming style that supports code as a model, makes debugging easy and is consistent with other popular scientific computing libraries, while remaining efficient and supporting hardware accelerators such as GPUs. In this paper, we detail the principles that drove the implementation of PyTorch and how they are reflected in its architecture. We emphasize that every aspect of PyTorch is a regular Python program under the full control of its user. We also explain how the careful and pragmatic implementation of the key components of its runtime enables them to work together to achieve compelling performance. We demonstrate the efficiency of individual subsystems, as well as the overall speed of PyTorch on several commonly used benchmarks.

SCALE-Net: Scalable Vehicle Trajectory Prediction Network under Random Number of Interacting Vehicles via Edge-enhanced Graph Convolutional Neural Network

2020-01-01
Hyeongseok Jeon , Junwon Choi , Dongsuk Kum
Predicting the future trajectory of surrounding vehicles in a randomly varying traffic level is one of the most challenging problems in developing an autonomous vehicle. Since there is no pre-defined … Predicting the future trajectory of surrounding vehicles in a randomly varying traffic level is one of the most challenging problems in developing an autonomous vehicle. Since there is no pre-defined number of interacting vehicles participate in, the prediction network has to be scalable with respect to the vehicle number in order to guarantee the consistency in terms of both accuracy and computational load. In this paper, the first fully scalable trajectory prediction network, SCALE-Net, is proposed that can ensure both higher prediction performance and consistent computational load regardless of the number of surrounding vehicles. The SCALE-Net employs the Edge-enhance Graph Convolutional Neural Network (EGCN) for the inter-vehicular interaction embedding network. Since the proposed EGCN is inherently scalable with respect to the graph node (an agent in this study), the model can be operated independently from the total number of vehicles considered. We evaluated the scalability of the SCALE-Net on the publically available NGSIM datasets by comparing variations on computation time and prediction accuracy per single driving scene with respect to the varying vehicle number. The experimental test shows that both computation time and prediction performance of the SCALE-Net consistently outperform those of previous models regardless of the level of traffic complexities.
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On the Consistency of Bayes Estimates

1986-03-01
Persi Diaconis , David A. Freedman
We discuss frequency properties of Bayes rules, paying special attention to consistency. Some new and fairly natural counterexamples are given, involving nonparametric estimates of location. Even the Dirichlet prior can … We discuss frequency properties of Bayes rules, paying special attention to consistency. Some new and fairly natural counterexamples are given, involving nonparametric estimates of location. Even the Dirichlet prior can lead to inconsistent estimates if used too aggressively. Finally, we discuss reasons for Bayesians to be interested in frequency properties of Bayes rules. As a part of the discussion we give a subjective equivalent to consistency and compute the derivative of the map taking priors to posteriors.

Optimal Decentralized Control for Uncertain Systems by Symmetric Gauss–Seidel Semi-Proximal ALM

2021-10-26
Jun Ma , Zilong Cheng , Xiaoxue Zhang +2 more
The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math></inline-formula> -guaranteed cost decentralized control problem is investigated in this article. More specifically, on the basis of an appropriate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math></inline-formula> reformulation … The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math></inline-formula> -guaranteed cost decentralized control problem is investigated in this article. More specifically, on the basis of an appropriate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math></inline-formula> reformulation that we put in place, the optimal control problem in the presence of parameter uncertainties is then suitably characterized by convex restriction and solved in parameter space. It is shown that a set of stabilizing decentralized controller gains for the uncertain system is parameterized in a convex set through appropriate convex restriction, and then an approximated conic optimization problem is constructed. This facilitates the use of the symmetric Gauss–Seidel (sGS) semi-proximal augmented Lagrangian method (ALM), which attains high computational effectiveness. A comprehensive analysis is given on the application of the approach in solving the optimal decentralized control problem; and subsequently, the preserved decentralized structure, robust stability, and robust performance are all suitably guaranteed with the proposed methodology. Furthermore, an illustrative example is presented to demonstrate the effectiveness of the proposed optimization approach.
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An Integrated Framework of Decision Making and Motion Planning for Autonomous Vehicles Considering Social Behaviors

2020-11-25
Peng Hang , Chen Lv , Chao Huang +3 more
This paper presents a novel integrated approach to deal with the decision making and motion planning for lane-change maneuvers of autonomous vehicle (AV) considering social behaviors of surrounding traffic occupants. … This paper presents a novel integrated approach to deal with the decision making and motion planning for lane-change maneuvers of autonomous vehicle (AV) considering social behaviors of surrounding traffic occupants. Reflected by driving styles and intentions of surrounding vehicles, the social behaviors are taken into consideration during the modelling process. Then, the Stackelberg Game theory is applied to solve the decision-making, which is formulated as a non-cooperative game problem. Besides, potential field is adopted in the motion planning model, which uses different potential functions to describe surrounding vehicles with different behaviors and road constraints. Then, Model Predictive Control (MPC) is utilized to predict the state and trajectory of the autonomous vehicle. Finally, the decision-making and motion planning is then integrated into a constrained multi-objective optimization problem. Three testing scenarios considering different social behaviors of surrounding vehicles are carried out to validate the performance of the proposed approach. Testing results show that the integrated approach is able to address different social interactions with other traffic participants, and make proper and safe decisions and planning for autonomous vehicles, demonstrating its feasibility and effectiveness.
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Posterior consistency of Dirichlet mixtures in density estimation

1999-03-01
Subhashis Ghosal , Jayanta K. Ghosh , Ravi Ramamoorthi
A Dirichlet mixture of normal densities is a useful choice for a prior distribution on densities in the problem of Bayesian density estimation. In recent years, efficient Markov chain Monte … A Dirichlet mixture of normal densities is a useful choice for a prior distribution on densities in the problem of Bayesian density estimation. In recent years, efficient Markov chain Monte Carlo method for the computation of the posterior distribution has been developed. The method has been applied to data arising from different fields of interest. The important issue of consistency was however left open. In this paper, we settle this issue in affirmative.
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Pluricomplex energy

1998-01-01
Urban Cegrell
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Trajectory Generation by Chance-Constrained Nonlinear MPC With Probabilistic Prediction

2020-11-25
Xiaoxue Zhang , Jun Ma , Zilong Cheng +3 more
Continued great efforts have been dedicated toward high-quality trajectory generation based on optimization methods; however, most of them do not suitably and effectively consider the situation with moving obstacles; and … Continued great efforts have been dedicated toward high-quality trajectory generation based on optimization methods; however, most of them do not suitably and effectively consider the situation with moving obstacles; and more particularly, the future position of these moving obstacles in the presence of uncertainty within some possible prescribed prediction horizon. To cater to this rather major shortcoming, this work shows how a variational Bayesian Gaussian mixture model (vBGMM) framework can be employed to predict the future trajectory of moving obstacles; and then with this methodology, a trajectory generation framework is proposed which will efficiently and effectively address trajectory generation in the presence of moving obstacles, and incorporate the presence of uncertainty within a prediction horizon. In this work, the full predictive conditional probability density function (PDF) with mean and covariance is obtained and, thus, a future trajectory with uncertainty is formulated as a collision region represented by a confidence ellipsoid. To avoid the collision region, chance constraints are imposed to restrict the collision probability, and subsequently, a nonlinear model predictive control problem is constructed with these chance constraints. It is shown that the proposed approach is able to predict the future position of the moving obstacles effectively; and, thus, based on the environmental information of the probabilistic prediction, it is also shown that the timing of collision avoidance can be earlier than the method without prediction. The tracking error and distance to obstacles of the trajectory with prediction are smaller compared with the method without prediction.
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Consistency of Bernstein Polynomial Posteriors

2002-01-01
Sonia Petrone , Larry Wasserman
Summary A Bernstein prior is a probability measure on the space of all the distribution functions on [0, 1]. Under very general assumptions, it selects absolutely continuous distribution functions, whose … Summary A Bernstein prior is a probability measure on the space of all the distribution functions on [0, 1]. Under very general assumptions, it selects absolutely continuous distribution functions, whose densities are mixtures of known beta densities. The Bernstein prior is of interest in Bayesian nonparametric inference with continuous data. We study the consistency of the posterior from a Bernstein prior. We first show that, under mild assumptions, the posterior is weakly consistent for any distribution function P0 on [0, 1] with continuous and bounded Lebesgue density. With slightly stronger assumptions on the prior, the posterior is also Hellinger consistent. This implies that the predictive density from a Bernstein prior, which is a Bayesian density estimate, converges in the Hellinger sense to the true density (assuming that it is continuous and bounded). We also study a sieve maximum likelihood version of the density estimator and show that it is also Hellinger consistent under weak assumptions. When the order of the Bernstein polynomial, i.e. the number of components in the beta distribution mixture, is truncated, we show that under mild restrictions the posterior concentrates on the set of pseudotrue densities. Finally, we study the behaviour of the predictive density numerically and we also study a hybrid Bayes–maximum likelihood density estimator.
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Convergence rates of nonparametric posterior distributions

2010-10-29
Yang Xing
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On the Asymptotic Behavior of Bayes' Estimates in the Discrete Case

1963-12-01
David A. Freedman
Doob (1949) obtained a very general result on the consistency of Bayes' estimates. Loosely, if any consistent estimates are available, then the Bayes' estimates are consistent for almost all values … Doob (1949) obtained a very general result on the consistency of Bayes' estimates. Loosely, if any consistent estimates are available, then the Bayes' estimates are consistent for almost all values of the parameter under the prior measure. If the parameter is thought of as being selected by nature through a random mechanism whose probability law is known, Doob's result is completely satisfactory. On the other hand, in some circumstances it is necessary to identify the exceptional null set. For example, if the parameter is thought of as fixed but unknown, and the prior measure is chosen as a convenient way to calculate estimates, it is important to know for which null set the method fails. In particular, it is desirable to choose the prior so that the null set is in fact empty. The problem is very delicate; considerable work [8], [9], [12] has been done on it recently, in quite general contexts and under severe regularity assumptions. It might therefore be of interest to discuss the simplest possible case, that of independent, identically distributed, discrete observations, in some detail. This will be done in Sections 3 and 4 when the observations take a finite set of possible values. Under this assumption, Section 3 shows that the posterior probability converges to point mass at the true parameter value among almost all sample sequences (for short, the posterior is consistent; see Definition 1) exactly for parameter values in the topological carrier of the prior. In Section 4, the asymptotic normality of the posterior is shown to follow from a local smoothness assumption about the prior. In both sections, results are obtained for priors which admit the possibility of an infinite number of states. The results of these sections are not entirely new; see pp. 333 ff. of [7], pp. 224 ff. of [10], [11]. They have not appeared in the literature, to the best of our knowledge, in a form as precise as Theorems 1, 3, 4. Theorem 2 is essentially the relevant special case of Theorem 7.4 of Schwartz (1961). In Sections 5 and 6, the case of a countable number of possible values is treated. We believe the results to be new. Here the general problem appears, because priors which assign positive mass near the true parameter value may lead to ridiculous estimates. The results of Section 3 (let alone 4) are false. In fact, Theorem 5 of Section 5 gives the following construction. Suppose that under the true parameter value the observations take an infinite number of values with positive probability. Then given any spurious (sub-)stochastic probability distribution, it is possible to find a prior assigning positive mass to any neighborhood of the true parameter value, but leading to a posterior probability which converges for almost all sample sequences to point mass at the spurious distribution. Indeed, there is a prior assigning positive mass to every open set of parameters, for which the posterior is consistent only at a set of parameters of the first category. To some extent, this happens because at any stage information about a finite number of stages only is available, but on the basis of this evidence, conclusions must be drawn about all states. If the prior measure has a serious prejudice about the shape of the tails, disaster ensues. In Section 6, it is shown that a simple condition on the prior measure (which serves to limit this prejudice) ensures the consistency of the posterior. Prior probabilities leading to posterior distributions consistent at all and asymptotically normal at essentially all (see Remark 3, Section 3) parameter values are constructed. Section 5 is independent of Sections 3 and 4; Section 6 is not. Section 6 overlaps to some extent with unpublished work of Kiefer and Wolfowitz; it has been extended in certain directions by Fabius (1963). The results of this paper were announced in [5]; some related work for continuous state space is described in [3]. It is a pleasure to thank two very helpful referees: whatever expository merit Section 5 has is due to them and to L. J. Savage.
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Fast Graph Representation Learning with PyTorch Geometric

2019-03-06
Matthias Fey , Jan Eric Lenssen
We introduce PyTorch Geometric, a library for deep learning on irregularly structured input data such as graphs, point clouds and manifolds, built upon PyTorch. In addition to general graph data … We introduce PyTorch Geometric, a library for deep learning on irregularly structured input data such as graphs, point clouds and manifolds, built upon PyTorch. In addition to general graph data structures and processing methods, it contains a variety of recently published methods from the domains of relational learning and 3D data processing. PyTorch Geometric achieves high data throughput by leveraging sparse GPU acceleration, by providing dedicated CUDA kernels and by introducing efficient mini-batch handling for input examples of different size. In this work, we present the library in detail and perform a comprehensive comparative study of the implemented methods in homogeneous evaluation scenarios.

Convergence rates of posterior distributions for noniid observations

2007-02-01
Subhashis Ghosal , Aad van der Vaart
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the … We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the posterior measure relative to distances derived from a testing criterion. We then specialize our results to independent, nonidentically distributed observations, Markov processes, stationary Gaussian time series and the white noise model. We apply our general results to several examples of infinite-dimensional statistical models including nonparametric regression with normal errors, binary regression, Poisson regression, an interval censoring model, Whittle estimation of the spectral density of a time series and a nonlinear autoregressive model.
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Continuity of the complex Monge-Ampère operator

1996-01-01
Yang Xing
The complex Monge-Ampère operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis d d Superscript c Baseline right-parenthesis Superscript n"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> … The complex Monge-Ampère operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis d d Superscript c Baseline right-parenthesis Superscript n"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">(dd^c)^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an important tool in complex analysis. It would be interesting to find the right notion of convergence <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u Subscript j Baseline right-arrow u"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mo stretchy="false">→</mml:mo> <mml:mi>u</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">u_j\to u</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis d d Superscript c Baseline u Subscript j Baseline right-parenthesis Superscript n Baseline right-arrow left-parenthesis d d Superscript c Baseline u right-parenthesis Superscript n"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="false">→</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:mi>u</mml:mi> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">(dd^cu_j)^n\to (dd^cu)^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in the weak topology. In this paper, using the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript n minus 1"> <mml:semantics> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">C_{n-1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-capacity, we give a sufficient condition of the weak convergence <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis d d Superscript c Baseline u Subscript j Baseline right-parenthesis Superscript n Baseline right-arrow left-parenthesis d d Superscript c Baseline u right-parenthesis Superscript n"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="false">→</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> </mml:msup> <mml:mi>u</mml:mi> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">(dd^cu_j)^n\to (dd^cu)^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We also show that our condition is quite sharp in some case.
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ReCoG: A Deep Learning Framework with Heterogeneous Graph for Interaction-Aware Trajectory Prediction

2020-01-01
Xiaoyu Mo , Yang Xing , Chen Lv
Predicting the future trajectory of surrounding vehicles is essential for the navigation of autonomous vehicles in complex real-world driving scenarios. It is challenging as a vehicle's motion is affected by … Predicting the future trajectory of surrounding vehicles is essential for the navigation of autonomous vehicles in complex real-world driving scenarios. It is challenging as a vehicle's motion is affected by many factors, including its surrounding infrastructures and vehicles. In this work, we develop the ReCoG (Recurrent Convolutional and Graph Neural Networks), which is a general scheme that represents vehicle interactions with infrastructure information as a heterogeneous graph and applies graph neural networks (GNNs) to model the high-level interactions for trajectory prediction. Nodes in the graph contain corresponding features, where a vehicle node contains its sequential feature encoded using Recurrent Neural Network (RNN), and an infrastructure node contains spatial feature encoded using Convolutional Neural Network (CNN). Then the ReCoG predicts the future trajectory of the target vehicle by jointly considering all of the features. Experiments are conducted by using the INTERACTION dataset. Experimental results show that the proposed ReCoG outperforms other state-of-the-art methods in terms of different types of displacement error, validating the feasibility and effectiveness of the developed approach.

Fine topology, Šilov boundary, and (ddc)n

1987-06-01
Eric Bedford , B. A. Taylor

The ApolloScape Open Dataset for Autonomous Driving and Its Application

2019-07-07
Xinyu Huang , Peng Wang , Xinjing Cheng +3 more
Autonomous driving has attracted tremendous attention especially in the past few years. The key techniques for a self-driving car include solving tasks like 3D map construction, self-localization, parsing the driving … Autonomous driving has attracted tremendous attention especially in the past few years. The key techniques for a self-driving car include solving tasks like 3D map construction, self-localization, parsing the driving road and understanding objects, which enable vehicles to reason and act. However, large scale data set for training and system evaluation is still a bottleneck for developing robust perception models. In this paper, we present the ApolloScape dataset [1] and its applications for autonomous driving. Compared with existing public datasets from real scenes, e.g. KITTI [2] or Cityscapes [3], ApolloScape contains much large and richer labelling including holistic semantic dense point cloud for each site, stereo, per-pixel semantic labelling, lanemark labelling, instance segmentation, 3D car instance, high accurate location for every frame in various driving videos from multiple sites, cities and daytimes. For each task, it contains at lease 15x larger amount of images than SOTA datasets. To label such a complete dataset, we develop various tools and algorithms specified for each task to accelerate the labelling process, such as 3D-2D segment labeling tools, active labelling in videos etc. Depend on ApolloScape, we are able to develop algorithms jointly consider the learning and inference of multiple tasks. In this paper, we provide a sensor fusion scheme integrating camera videos, consumer-grade motion sensors (GPS/IMU), and a 3D semantic map in order to achieve robust self-localization and semantic segmentation for autonomous driving. We show that practically, sensor fusion and joint learning of multiple tasks are beneficial to achieve a more robust and accurate system. We expect our dataset and proposed relevant algorithms can support and motivate researchers for further development of multi-sensor fusion and multi-task learning in the field of computer vision.
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Convergence rates for Bayesian density estimation of infinite-dimensional exponential families

2006-12-01
Catia Scricciolo
We study the rate of convergence of posterior distributions in density estimation problems for log-densities in periodic Sobolev classes characterized by a smoothness parameter p. The posterior expected density provides … We study the rate of convergence of posterior distributions in density estimation problems for log-densities in periodic Sobolev classes characterized by a smoothness parameter p. The posterior expected density provides a nonparametric estimation procedure attaining the optimal minimax rate of convergence under Hellinger loss if the posterior distribution achieves the optimal rate over certain uniformity classes. A prior on the density class of interest is induced by a prior on the coefficients of the trigonometric series expansion of the log-density. We show that when p is known, the posterior distribution of a Gaussian prior achieves the optimal rate provided the prior variances die off sufficiently rapidly. For a mixture of normal distributions, the mixing weights on the dimension of the exponential family are assumed to be bounded below by an exponentially decreasing sequence. To avoid the use of infinite bases, we develop priors that cut off the series at a sample-size-dependent truncation point. When the degree of smoothness is unknown, a finite mixture of normal priors indexed by the smoothness parameter, which is also assigned a prior, produces the best rate. A rate-adaptive estimator is derived.
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On rates of convergence for posterior distributions in infinite-dimensional models

2007-04-01
Stephen G. Walker , Antonio Lijoi , Igor Prünster
This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian … This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of convergence for models including the mixture of Dirichlet process model and the random Bernstein polynomial model.
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Plurisubharmonic Functions and Potential Theory in Several Complex Variables

2000-01-01
Christer O. Kiselman
We survey the development of the theory of plurisubharmonic func- tions and the potential theory associated with them from their emergence in 1942 to 1997. We survey the development of the theory of plurisubharmonic func- tions and the potential theory associated with them from their emergence in 1942 to 1997.

Sur la définition de l'opérateur de Monge-Ampère complexe

1984-01-01
Christer O. Kiselman

On the dirichlet problem for the complex Monge-Amp�re operator

1984-06-01
Urban Cegrell

Posterior convergence rates of Dirichlet mixtures at smooth densities

2007-04-01
Subhashis Ghosal , Aad van der Vaart
We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be … We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be twice continuously differentiable. The bandwidth is given a sequence of priors which is obtained by scaling a single prior by an appropriate order. In order to handle this problem, we derive a new general rate theorem by considering a countable covering of the parameter space whose prior probabilities satisfy a summability condition together with certain individual bounds on the Hellinger metric entropy. We apply this new general theorem on posterior convergence rates by computing bounds for Hellinger (bracketing) entropy numbers for the involved class of densities, the error in the approximation of a smooth density by normal mixtures and the concentration rate of the prior. The best obtainable rate of convergence of the posterior turns out to be equivalent to the well-known frequentist rate for integrated mean squared error n−2/5 up to a logarithmic factor.
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TNT: Target-driveN Trajectory Prediction

2020-01-01
Hang Zhao , Jiyang Gao , Tian Lan +7 more
Predicting the future behavior of moving agents is essential for real world applications. It is challenging as the intent of the agent and the corresponding behavior is unknown and intrinsically … Predicting the future behavior of moving agents is essential for real world applications. It is challenging as the intent of the agent and the corresponding behavior is unknown and intrinsically multimodal. Our key insight is that for prediction within a moderate time horizon, the future modes can be effectively captured by a set of target states. This leads to our target-driven trajectory prediction (TNT) framework. TNT has three stages which are trained end-to-end. It first predicts an agent's potential target states $T$ steps into the future, by encoding its interactions with the environment and the other agents. TNT then generates trajectory state sequences conditioned on targets. A final stage estimates trajectory likelihoods and a final compact set of trajectory predictions is selected. This is in contrast to previous work which models agent intents as latent variables, and relies on test-time sampling to generate diverse trajectories. We benchmark TNT on trajectory prediction of vehicles and pedestrians, where we outperform state-of-the-art on Argoverse Forecasting, INTERACTION, Stanford Drone and an in-house Pedestrian-at-Intersection dataset.

On sufficient conditions for Bayesian consistency

2003-06-01
Stephen G. Walker
This paper contributes to the theory of Bayesian consistency for a sequence of posterior and predictive distributions arising from an independent and identically distributed sample. A new sufficient condition for … This paper contributes to the theory of Bayesian consistency for a sequence of posterior and predictive distributions arising from an independent and identically distributed sample. A new sufficient condition for posterior Hellinger consistency is presented which provides motivation for recent results appearing in the literature. Such motivation is important since current sufficient conditions are not known to be necessary. It also provides new insights into Bayesian consistency. A new consistency theorem for the sequence of predictive densities is given.

Game-Theoretic Modeling of Traffic in Unsignalized Intersection Network for Autonomous Vehicle Control Verification and Validation

2020-11-17
Ran Tian , Nan Li , Ilya Kolmanovsky +2 more
For a foreseeable future, autonomous vehicles (AVs) will operate in traffic together with human-driven vehicles. Their planning and control systems need extensive testing, including early-stage testing in simulations where the … For a foreseeable future, autonomous vehicles (AVs) will operate in traffic together with human-driven vehicles. Their planning and control systems need extensive testing, including early-stage testing in simulations where the interactions among autonomous/human-driven vehicles are represented. Motivated by the need for such simulation tools, we propose a game-theoretic approach to modeling vehicle interactions, in particular, for urban traffic environments with unsignalized intersections. We develop traffic models with heterogeneous (in terms of their driving styles) and interactive vehicles based on our proposed approach, and use them for virtual testing, evaluation, and calibration of AV control systems. For illustration, we consider two AV control approaches, analyze their characteristics and performance based on the simulation results with our developed traffic models, and optimize the parameters of one of them.
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Fonctions Plurisousharmoniques Et Formes Differentielles Positives

2011-01-01
P. Lelong

Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling

2014-01-01
Jun‐Young Chung , Çağlar Gülçehre , Kyunghyun Cho +1 more
In this paper we compare different types of recurrent units in recurrent neural networks (RNNs). Especially, we focus on more sophisticated units that implement a gating mechanism, such as a … In this paper we compare different types of recurrent units in recurrent neural networks (RNNs). Especially, we focus on more sophisticated units that implement a gating mechanism, such as a long short-term memory (LSTM) unit and a recently proposed gated recurrent unit (GRU). We evaluate these recurrent units on the tasks of polyphonic music modeling and speech signal modeling. Our experiments revealed that these advanced recurrent units are indeed better than more traditional recurrent units such as tanh units. Also, we found GRU to be comparable to LSTM.

Random Bernstein Polynomials

1999-09-01
Sonia Petrone
Random Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on … Random Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on the space of distribution functions on [0, 1] which has full support and can easily select absolutely continuous distribution functions with a continuous and smooth derivative. In particular, the Bernstein polynomial which approximates a Dirichlet process is studied. This may be of interest in Bayesian non‐parametric inference. In the second part of the paper, we study the posterior from a “Bernstein–Dirichlet” prior and suggest a hybrid Monte Carlo approximation of it. The proposed algorithm has some aspects of novelty since the problem under examination has a “changing dimension” parameter space.

On adaptive Bayesian inference

2008-01-01
Yang Xing
We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of … We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general in-probability theorems on the rate of convergence of the resulting posterior distributions. We extend their results to almost sure assertions. As an application we study log spline densities with a finite number of models and obtain that the Bayes procedure achieves the optimal minimax rate n−γ/(2γ+1) of convergence if the true density of the observations belongs to the Hölder space Cγ[0,1]. This strengthens a result in [1; 2]. We also study consistency of posterior distributions of the model index and give conditions ensuring that the posterior distributions concentrate their masses near the index of the best model.
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Asymptotic Inference for Mixture Models by Using Data-Dependent Priors

2000-01-01
L. H. Wasserman
Summary For certain mixture models, improper priors are undesirable because they yield improper posteriors. However, proper priors may be undesirable because they require subjective input. We propose the use of … Summary For certain mixture models, improper priors are undesirable because they yield improper posteriors. However, proper priors may be undesirable because they require subjective input. We propose the use of specially chosen data-dependent priors. We show that, in some cases, data-dependent priors are the only priors that produce intervals with second-order correct frequentist coverage. The resulting posterior also has another interpretation: it is the product of a fixed prior and a pseudolikelihood.
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Adaptive Game-Theoretic Decision Making for Autonomous Vehicle Control at Roundabouts

2018-12-01
Ran Tian , Sisi Li , Nan Li +3 more
In this paper, we propose a decision making algorithm for autonomous vehicle control at a roundabout intersection. The algorithm is based on a game-theoretic model representing the interactions between the … In this paper, we propose a decision making algorithm for autonomous vehicle control at a roundabout intersection. The algorithm is based on a game-theoretic model representing the interactions between the ego vehicle and an opponent vehicle, and adapts to an online estimated driver type of the opponent vehicle. Simulation results are reported.
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Adam: A Method for Stochastic Optimization

2014-01-01
Diederik P. Kingma , Jimmy Ba
We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has … We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.
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The dirichlet problem for a complex Monge-Amp�re equation

1976-02-01
Eric Bedford , B. A. Taylor
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Cooperative Driving at Unsignalized Intersections Using Tree Search

2019-09-25
Huile Xu , Yi Zhang , Li Li +1 more
In this paper, we propose a new cooperative driving strategy for connected and automated vehicles (CAVs) at unsignalized intersections. Based on the tree representation of the solution space for the … In this paper, we propose a new cooperative driving strategy for connected and automated vehicles (CAVs) at unsignalized intersections. Based on the tree representation of the solution space for the passing order, we combine Monte Carlo tree search (MCTS) and some heuristic rules to find a nearly global-optimal passing order (leaf node) within a very short planning time. Testing results show that this new strategy can keep a good tradeoff between performance and computation flexibility.
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Efficient Evolutionary Algorithm for Single-Objective Bilevel Optimization

2013-01-01
Ankur Sinha , Pekka Malo , Kalyanmoy Deb
Bilevel optimization problems are a class of challenging optimization problems, which contain two levels of optimization tasks. In these problems, the optimal solutions to the lower level problem become possible … Bilevel optimization problems are a class of challenging optimization problems, which contain two levels of optimization tasks. In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the upper level problem. Such a requirement makes the optimization problem difficult to solve, and has kept the researchers busy towards devising methodologies, which can efficiently handle the problem. Despite the efforts, there hardly exists any effective methodology, which is capable of handling a complex bilevel problem. In this paper, we introduce bilevel evolutionary algorithm based on quadratic approximations (BLEAQ) of optimal lower level variables with respect to the upper level variables. The approach is capable of handling bilevel problems with different kinds of complexities in relatively smaller number of function evaluations. Ideas from classical optimization have been hybridized with evolutionary methods to generate an efficient optimization algorithm for generic bilevel problems. The efficacy of the algorithm has been shown on two sets of test problems. The first set is a recently proposed SMD test set, which contains problems with controllable complexities, and the second set contains standard test problems collected from the literature. The proposed method has been evaluated against two benchmarks, and the performance gain is observed to be significant.

Large-Sample Inference for Log-Spline Models

1990-06-01
Charles J. Stone
Let $f$ be a continuous and positive unknown density on a known compact interval $\mathscr{Y}$. Let $F$ denote the distribution function of $f$ and let $Q = F^{-1}$ denote its … Let $f$ be a continuous and positive unknown density on a known compact interval $\mathscr{Y}$. Let $F$ denote the distribution function of $f$ and let $Q = F^{-1}$ denote its quantile function. A finite-parameter exponential family model based on $B$-splines is constructed. Maximum-likelihood estimation of the parameters of the model based on a random sample of size $n$ from $f$ yields estimates $\hat{f, F}$ and $\hat{Q}$ of $f, F$ and $Q$, respectively. Under mild conditions, if the number of parameters tends to infinity in a suitable manner as $n \rightarrow \infty$, these estimates achieve the optimal rate of convergence. The asymptotic behavior of the corresponding confidence bounds is also investigated. In particular, it is shown that the standard errors of $\hat{F}$ and $\hat{Q}$ are asymptotically equal to those of the usual empirical distribution function and empirical quantile function.
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Exploiting Edge Features for Graph Neural Networks

2019-06-01
Liyu Gong , Qiang Cheng
Edge features contain important information about graphs. However, current state-of-the-art neural network models designed for graph learning, \eg, graph convolutional networks (GCN) and graph attention networks (GAT), inadequately utilize edge … Edge features contain important information about graphs. However, current state-of-the-art neural network models designed for graph learning, \eg, graph convolutional networks (GCN) and graph attention networks (GAT), inadequately utilize edge features, especially multi-dimensional edge features. In this paper, we build a new framework for a family of new graph neural network models that can more sufficiently exploit edge features, including those of undirected or multi-dimensional edges. The proposed framework can consolidate current graph neural network models, e.g., GCN and GAT. The proposed framework and new models have the following novelties: First, we propose to use doubly stochastic normalization of graph edge features instead of the commonly used row or symmetric normalization approaches used in current graph neural networks. Second, we construct new formulas for the operations in each individual layer so that they can handle multi-dimensional edge features. Third, for the proposed new framework, edge features are adaptive across network layers. As a result, our proposed new framework and new models are able to exploit a rich source of graph edge information. We apply our new models to graph node classification on several citation networks, whole graph classification, and regression on several molecular datasets. Compared with the current state-of-the-art methods, i.e., GCNs and GAT, our models obtain better performance, which testify to the importance of exploiting edge features in graph neural networks.
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INTERACTION Dataset: An INTERnational, Adversarial and Cooperative moTION Dataset in Interactive Driving Scenarios with Semantic Maps

2019-01-01
Wei Zhan , Liting Sun , Di Wang +7 more
Behavior-related research areas such as motion prediction/planning, representation/imitation learning, behavior modeling/generation, and algorithm testing, require support from high-quality motion datasets containing interactive driving scenarios with different driving cultures. In this … Behavior-related research areas such as motion prediction/planning, representation/imitation learning, behavior modeling/generation, and algorithm testing, require support from high-quality motion datasets containing interactive driving scenarios with different driving cultures. In this paper, we present an INTERnational, Adversarial and Cooperative moTION dataset (INTERACTION dataset) in interactive driving scenarios with semantic maps. Five features of the dataset are highlighted. 1) The interactive driving scenarios are diverse, including urban/highway/ramp merging and lane changes, roundabouts with yield/stop signs, signalized intersections, intersections with one/two/all-way stops, etc. 2) Motion data from different countries and different continents are collected so that driving preferences and styles in different cultures are naturally included. 3) The driving behavior is highly interactive and complex with adversarial and cooperative motions of various traffic participants. Highly complex behavior such as negotiations, aggressive/irrational decisions and traffic rule violations are densely contained in the dataset, while regular behavior can also be found from cautious car-following, stop, left/right/U-turn to rational lane-change and cycling and pedestrian crossing, etc. 4) The levels of criticality span wide, from regular safe operations to dangerous, near-collision maneuvers. Real collision, although relatively slight, is also included. 5) Maps with complete semantic information are provided with physical layers, reference lines, lanelet connections and traffic rules. The data is recorded from drones and traffic cameras. Statistics of the dataset in terms of number of entities and interaction density are also provided, along with some utilization examples in a variety of behavior-related research areas. The dataset can be downloaded via https://interaction-dataset.com.