Safe-Bayesian Generalized Linear Regression
Abstract
We study generalized Bayesian inference under misspecification, i.e. when the model is ‘wrong but useful’. Generalized Bayes equips the likelihood with a learning rate $\eta$. We show that for generalized linear models (GLMs), $\eta$-generalized Bayes concentrates around the best approximation of the truth within the model for specific $\eta eq 1$, even under severely misspecified noise, as long as the tails of the true distribution are exponential. We derive MCMC samplers for generalized Bayesian lasso and logistic regression and give examples of both simulated and real-world data in which generalized Bayes substantially outperforms standard Bayes.
Cite
Text
Heide et al. "Safe-Bayesian Generalized Linear Regression." Artificial Intelligence and Statistics, 2020.Markdown
[Heide et al. "Safe-Bayesian Generalized Linear Regression." Artificial Intelligence and Statistics, 2020.](https://mlanthology.org/aistats/2020/heide2020aistats-safebayesian/)BibTeX
@inproceedings{heide2020aistats-safebayesian,
title = {{Safe-Bayesian Generalized Linear Regression}},
author = {Heide, Rianne and Kirichenko, Alisa and Grunwald, Peter and Mehta, Nishant},
booktitle = {Artificial Intelligence and Statistics},
year = {2020},
pages = {2623-2633},
volume = {108},
url = {https://mlanthology.org/aistats/2020/heide2020aistats-safebayesian/}
}