Variational Bayesian State-Space Models (aka Linear Dynamical Systems) 
v3.4.1
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.
Additions in v3.4.1 (03/29/05) since v3.0 (08/11/03)
- Function to compute posterior distributions over ABCD block matrix and CB+D parameters.
- Function to compute significance of these distributions for structure determination.
- Functions to compute ROC and AUC measurements of an inferred structure from a known structure.
- Codebase rewritten to include (optional) modifications to ARD prior to incorporate expert external knowledge:
- on observed correlations,
- and also on hidden correlations (thus indentifying hidden states).
In upcoming releases v3.4.1+
- Provide sample scripts to demonstrate features new in release v3.4.1
- Allow missing (unobserved) entire time points in the data (smooth, predict, and feedback).
- Allow for missing individual dimensions at some time points (sensor failure).
To appear on or before April 1 2006. Download, unzip and extract the vbssm341.tgz file for vbssm functions (use tar -xvzf vbssm341.tgz).
You are strongly recommended to consult chapter 5 of my thesis to understand the code.
Follow the included readme file for help.
Link to relevant papers
-
Beal, M.J., Falciani, F., Ghahramani Z., Rangel, C. and Wild, D.L.
A Bayesian Approach to Reconstructing Genetic Regulatory Networks with Hidden Factors
In Bioinformatics 21:349-356, 2005.
[abstract] [pdf] supplementary data page VBLDS software -
Beal, M.J.
Variational Algorithms for Approximate Bayesian Inference
PhD. Thesis, Gatsby Computational Neuroscience Unit, University College London, 2003. (281 pages)
[pdf] [ps.gz] or as individual chapters:
test IntroductionCh 2: Variational Bayesian Theory (38) [pdf 491k] [ps.gz 379k] Ch 5: Variational Bayesian Linear Dynamical Systems (47) [pdf 1.1M] [ps.gz 1.3M] -
Ghahramani, Z. and Beal, M.J.
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]
Acknowledgement: This material is based upon work supported by the National Science Foundation under Grant No. 0524331.
Disclaimer: Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).