Artificial Intelligence Review

, Volume 38, Issue 2, pp 85–95

A tutorial on variational Bayesian inference


DOI: 10.1007/s10462-011-9236-8

Cite this article as:
Fox, C.W. & Roberts, S.J. Artif Intell Rev (2012) 38: 85. doi:10.1007/s10462-011-9236-8


This tutorial describes the mean-field variational Bayesian approximation to inference in graphical models, using modern machine learning terminology rather than statistical physics concepts. It begins by seeking to find an approximate mean-field distribution close to the target joint in the KL-divergence sense. It then derives local node updates and reviews the recent Variational Message Passing framework.


Variational Bayes Mean-field Tutorial 

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Adaptive Behaviour Research GroupUniversity of SheffieldSheffieldUK
  2. 2.Pattern Analysis and Machine Learning Research Group, Department of Engineering ScienceUniversity of OxfordOxfordUK

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