PAC$^m$-Bayes: Narrowing the Empirical Risk Gap in the Misspecified Bayesian Regime
Autor: | Morningstar, Warren R., Alemi, Alexander A., Dillon, Joshua V. |
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Rok vydání: | 2020 |
Předmět: | |
Zdroj: | International Conference on Artificial Intelligence and Statistics, 8270-8298, (2022) |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: Accepted at AISTATS2022 |
Databáze: | arXiv |
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