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arXiv · 2010.09629

PAC$^m$-Bayes: Narrowing the Empirical Risk Gap in the Misspecified Bayesian Regime

Warren R. Morningstar·Alexander A. Alemi·Joshua V. Dillon
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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. However 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.

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BibTeXRIS

Warren R. Morningstar, Alexander A. Alemi, Joshua V. Dillon. 2020-10-19. PAC$^m$-Bayes: Narrowing the Empirical Risk Gap in the Misspecified Bayesian Regime. https://arxiv.org/abs/2010.09629

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