# Safe-Bayesian Generalized Linear Regression

arXiv: https://arxiv.org/abs/1910.09227 · HTML: https://mlsanity.com/paper/1910.09227/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2019.

## Built on by (most cited first, 9 of 9)

- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Optimistic Information Directed Sampling](https://mlsanity.com/paper/2402.15411/) (2024)
- [Active multi-fidelity Bayesian online changepoint detection](https://mlsanity.com/paper/2103.14224/) (2021)
- [Variational Inference of overparameterized Bayesian Neural Networks: a theoretical and empirical study](https://mlsanity.com/paper/2207.03859/) (2022)
- [Posterior concentration and fast convergence rates for generalized Bayesian learning](https://mlsanity.com/paper/2111.10243/) (2021)
- [Reproducible Parameter Inference Using Bagged Posteriors](https://mlsanity.com/paper/2311.02019/) (2023)
- [Excess risk analysis for epistemic uncertainty with application to variational inference](https://mlsanity.com/paper/2206.01606/) (2022)
- [In all LikelihoodS: How to Reliably Select Pseudo-Labeled Data for Self-Training in Semi-Supervised Learning](https://mlsanity.com/paper/2303.01117/) (2023)
- [Addressing the Inconsistency in Bayesian Deep Learning via Generalized Laplace Approximation](https://mlsanity.com/paper/2405.13535/) (2024)

## Abstract (arXiv)

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 η. We show that for generalized linear models (GLMs), η-generalized Bayes concentrates around the best approximation of the truth within the model for specific η neq 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.