# Variational Bayesian inference for linear and logistic regression

arXiv: https://arxiv.org/abs/1310.5438 · HTML: https://mlsanity.com/paper/1310.5438/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2013.

## Built on by (most cited first, 4 of 4)

- [A flexible empirical Bayes approach to multiple linear regression and connections with penalized regression](https://mlsanity.com/paper/2208.10910/) (2022)
- [Sparse online variational Bayesian regression](https://mlsanity.com/paper/2102.12261/) (2021)
- [Use of Variational Inference in Music Emotion Recognition](https://mlsanity.com/paper/2106.14323/) (2021)
- [Robust Variational Bayes by Min-Max Median Aggregation](https://mlsanity.com/paper/2512.12676/) (2025)

## Abstract (arXiv)

The article describe the model, derivation, and implementation of variational Bayesian inference for linear and logistic regression, both with and without automatic relevance determination. It has the dual function of acting as a tutorial for the derivation of variational Bayesian inference for simple models, as well as documenting, and providing brief examples for the MATLAB/Octave functions that implement this inference. These functions are freely available online.