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Contributed Talk
Workshop: Your Model is Wrong: Robustness and misspecification in probabilistic modeling

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

Alexander Alemi


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.