Posterior concentration and fast convergence rates for generalized Bayesian learning
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Abstract (arXiv)
In this paper, we study the learning rate of generalized Bayes estimators in a general setting where the hypothesis class can be uncountable and have an irregular shape, the loss function can have heavy tails, and the optimal hypothesis may not be unique. We prove that under the multi-scale Bernstein's condition, the generalized posterior distribution concentrates around the set of optimal hypotheses and the generalized Bayes estimator can achieve fast learning rate. Our results are applied to show that the standard Bayesian linear regression is robust to heavy-tailed distributions.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 14 of its 41 references that are in the map. First posted on arXiv 19 Nov 2021.
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14 of 41 references.
References · 14
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- 2016PAC-Bayesian Theory Meets Bayesian Inferencecited by 87
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- 2014Learning without Concentrationcited by 50
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- 2014Empirical risk minimization for heavy-tailed lossescited by 37
- 2019Safe-Bayesian Generalized Linear Regressioncited by 9
- 2015On aggregation for heavy-tailed classescited by 7
- 2014Generalization and Robustness of Batched Weighted Average Algorithm with V-geometrically Ergodic Markov Datacited by 4
- 2014Learning From Non-iid Data: Fast Rates for the One-vs-All Multiclass Plug-in Classifierscited by 3
- 2014From Stochastic Mixability to Fast Ratescited by 2
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Citing papers per year: 2022: 1; 2023: 1.
2 papers.