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:
-
Beal, M.J., Ghahramani, Z. (2002)
The Variational Bayesian EM Algorithm for Incomplete Data: with Application to Scoring Graphical Model Structures
In Bayesian Statistics 7, Oxford University Press, 2003.
[pdf] [ps.gz]
and for more detail on the theory behind all of these pieces of code, see my thesis:
-
Beal, M.J. (2003)
Variational Algorithms for Approximate Bayesian Inference
PhD. Thesis, Gatsby Computational Neuroscience Unit, University College London, 2003.
thesis download page
Variational Bayesian State-Space Models (aka Linear Dynamical Systems) v3.0
[There is a more active page at http://www.cse.buffalo.edu/faculty/mbeal/vbsmm.html]
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:
-
Ghahramani, Z. and Beal, M.J. (2000)
Propagation Algorithms for Variational Bayesian Learning
In Advances in Neural Information Processing Systems 13, eds. T.K. Leen, T. Dietterich, V. Tresp, MIT Press, 2001.
[pdf] [ps.gz] [poster]
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The relevant paper for this code is an unpublished report: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
-
Ghahramani, Z. and Beal, M.J. (2000)
Variational Inference for Bayesian Mixtures of Factor Analysers
In Advances in Neural Information Processing Systems 12:449-455, eds. S. A. Solla, T.K. Leen, K. Müller, MIT Press, 2000.
[pdf] [ps.gz] [poster]
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.