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

• URL: http://arxiv.org/abs/2010.09629v3
• Date: Mon, 23 May 2022 17:05:06 GMT
• Title: PAC$^m$-Bayes: Narrowing the Empirical Risk Gap in the Misspecified Bayesian Regime
• Authors: Warren R. Morningstar, Alexander A. Alemi and Joshua V. Dillon
• Abstract summary: This work develops a multi-sample loss which can close the gap by spanning a trade-off between the two risks. Empirical study demonstrates improvement to the predictive distribution.
• Score: 75.19403612525811
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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