PACm-Bayes: Narrowing the Empirical Risk Gap in the Misspecified Bayesian Regime
Abstract
The Bayesian posterior minimizes the "inferential risk" which itself bounds the "predictive risk." This bound is tight when the likelihood and prior are well-specified. How-ever since misspecification induces a gap,the Bayesian posterior predictive distribution may have poor generalization performance. This work develops a multi-sample loss (PAC$^m$) which can close the gap by spanning a trade-off between the two risks. The loss is computationally favorable and offers PAC generalization guarantees. Empirical study demonstrates improvement to the predictive distribution
Cite
Text
Morningstar et al. " PACm-Bayes: Narrowing the Empirical Risk Gap in the Misspecified Bayesian Regime ." Artificial Intelligence and Statistics, 2022.Markdown
[Morningstar et al. " PACm-Bayes: Narrowing the Empirical Risk Gap in the Misspecified Bayesian Regime ." Artificial Intelligence and Statistics, 2022.](https://mlanthology.org/aistats/2022/morningstar2022aistats-pacmbayes/)BibTeX
@inproceedings{morningstar2022aistats-pacmbayes,
title = {{ PACm-Bayes: Narrowing the Empirical Risk Gap in the Misspecified Bayesian Regime }},
author = {Morningstar, Warren R. and Alemi, Alex and Dillon, Joshua V.},
booktitle = {Artificial Intelligence and Statistics},
year = {2022},
pages = {8270-8298},
volume = {151},
url = {https://mlanthology.org/aistats/2022/morningstar2022aistats-pacmbayes/}
}