期刊
STATISTICAL SCIENCE
卷 37, 期 3, 页码 425-442出版社
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/21-STS840
关键词
Bayesian inference; Bayesian neural networks; convergence diagnostics; Markov chain Monte Carlo; posterior predictive distribution
资金
- Laboratory Directed Research and Development Program of Oak Ridge National Laboratory
- U.S. Department of Energy [DE-AC0500OR22725]
This paper reviews the challenges of using MCMC methods in Bayesian neural networks and shows that valuable posterior predictive distributions can be obtained through MCMC sampling.
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 nonconverged 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.
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