Depth induces scale-averaging in overparameterized linear Bayesian neural networks
Depth induces scale-averaging in overparameterized linear Bayesian neural networks
Inference in deep Bayesian neural networks is only fully understood in the infinite-width limit, where the posterior flexibility afforded by increased depth washes out and the posterior predictive collapses to a shallow Gaussian process. Here, we interpret finite deep linear Bayesian neural networks as data-dependent scale mixtures of Gaussian process …