All code accessible from this page is Copyright © 1998-2003 Matthew J. Beal.

For a general paper discussing Variational Bayesian EM and Graphical Models, please look at:

and for more detail on the theory behind all of these pieces of code, see my thesis:

Variational Bayesian State-Space Models (aka Linear Dynamical Systems) v3.0

[There is a more active page at]

Implements an approximation to full Bayesian input-driven state-space models (aka linear dynamical systems), allowing dimensionality determination of the hidden state (and all parameters) via automatic relevance determination methods. The tar includes variational Kalman Filter and Smoother functions, which are called as subroutines. Aside from my thesis, a useful reference is:

Download, unzip and extract the vbssm.tgz file for vbssm functions (use tar -xvzf vbssm.tgz).

You are strongly recommended to consult chapter 5 of my thesis to understand the code.

Follow the included readme file for help.

Variational Bayesian Hidden Markov Models

The relevant paper for this code is an unpublished report:

Thanks to Zoubin Ghahramani and Andy Brown for writing parts of the code.

Download, unzip and extract the vbhmm.tar.gz file for vbhmm functions (use tar -xvzf vbhmm.tar.gz). To get started, type vbhmm_demo at the Matlab prompt, or type help vbhmm or help vbhmm_cF.

Variational Bayesian Mixtures of Factor Analysers

Performs discrete changes to model structure by birth and death of mixture components, and simultaneously continuously determines each component's latent-space dimensionalities via automatic relevance determination. The relevant citation is

Download, unzip and extract the vbmfa.tar.gz file for vbmfa functions.

The graphical model implemented is not exactly as in the NIPS paper; the better model looks like this.

Follow the included readme file for help.