# Gibbs posterior concentration rates under sub-exponential type losses

arXiv: https://arxiv.org/abs/2012.04505 · HTML: https://mlsanity.com/paper/2012.04505/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2020.

## Built on by (most cited first, 5 of 5)

- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Adaptive variational Bayes: Optimality, computation and applications](https://mlsanity.com/paper/2109.03204/) (2021)
- [Bayesian Additive Distribution Regression](https://mlsanity.com/paper/2603.06462/) (2026)
- [Generative Regression with IQ-BART](https://mlsanity.com/paper/2507.04168/) (2025)
- [PAC-Bayes Bounds for Gibbs Posteriors via Singular Learning Theory](https://mlsanity.com/paper/2604.17219/) (2026)

## Abstract (arXiv)

Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior computations, plus a potentially serious risk of model misspecification bias. Gibbs posterior distributions, on the other hand, offer direct, principled, probabilistic inference on quantities of interest through a loss function, not a model-based likelihood. Here we provide simple sufficient conditions for establishing Gibbs posterior concentration rates when the loss function is of a sub-exponential type. We apply these general results in a range of practically relevant examples, including mean regression, quantile regression, and sparse high-dimensional classification. We also apply these techniques in an important problem in medical statistics, namely, estimation of a personalized minimum clinically important difference.