On best approximation by multivariate ridge functions with applications
to generalized translation networks
On best approximation by multivariate ridge functions with applications
to generalized translation networks
We prove sharp upper and lower bounds for the approximation of Sobolev functions by sums of multivariate ridge functions, i.e., functions of the form $\mathbb{R}^d \ni x \mapsto \sum_{k=1}^n h_k(A_k x) \in \mathbb{R}$ with $h_k : \mathbb{R}^\ell \to \mathbb{R}$ and $A_k \in \mathbb{R}^{\ell \times d}$. We show that the order …