Posterior concentration and fast convergence rates for generalized Bayesian learning
| Autor: | Duy Nguyen, Binh T. Nguyen, Lam Si Tung Ho, Vu Dinh |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Bayes estimator
Information Systems and Management 05 social sciences Posterior probability 050301 education Estimator 02 engineering and technology Function (mathematics) Bayesian inference Statistics::Computation Computer Science Applications Theoretical Computer Science Bayes' theorem Artificial Intelligence Control and Systems Engineering 0202 electrical engineering electronic engineering information engineering Applied mathematics 020201 artificial intelligence & image processing Uncountable set Bayesian linear regression 0503 education Computer Science::Databases Software Mathematics |
| Zdroj: | Information Sciences. 538:372-383 |
| ISSN: | 0020-0255 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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