Variational Bayesian inference for linear and logistic regression

TL;DR

This paper presents a comprehensive tutorial and implementation of variational Bayesian inference methods for linear and logistic regression models, including automatic relevance determination, with practical MATLAB/Octave examples.

Contribution

It offers a detailed derivation, implementation, and practical examples of variational Bayesian inference for simple regression models, serving as both a tutorial and a resource.

Findings

Provides MATLAB/Octave functions for variational Bayesian inference

Demonstrates inference for linear and logistic regression models

Includes automatic relevance determination techniques

Abstract

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.