Challenges in Markov chain Monte Carlo for Bayesian neural networks

TL;DR

This paper discusses the challenges of using MCMC for Bayesian neural networks, showing that even non-converged chains can produce accurate predictive distributions, highlighting a potential research direction despite convergence issues.

Contribution

It demonstrates that non-converged MCMC chains can still generate valuable predictive distributions in Bayesian neural networks, challenging the focus on convergence.

Findings

Non-converged MCMC chains can produce accurate predictive distributions.

Challenges in convergence limit the use of MCMC for exact posterior estimation.

Posterior predictive distributions remain valuable despite convergence issues.

Abstract

Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such challenges culminate to lack of convergence to the parameter posterior. Nevertheless, this paper shows that a non-converged Markov chain, generated via MCMC sampling from the parameter space of a neural network, can yield via Bayesian marginalization a valuable posterior predictive distribution of the output of the neural network. Classification examples based on multilayer perceptrons showcase highly accurate posterior predictive distributions. The postulate of limited scope for MCMC developments in BNNs is partially valid; an asymptotically exact parameter posterior seems less plausible, yet an accurate posterior predictive distribution is a tenable research avenue.