Variational Bayesian Mixtures of Factor Analysers
			   (version 1)
		    (C) Matthew J. Beal, 2000

		    www.gatsby.ucl.ac.uk/~beal
		     m.beal@gatsby.ucl.ac.uk

VBMFA is a variational approximation to a full* Bayesian implementation
of Mixtures of Factor Analysers. Included in this tar file are

  o the NIPS'99 paper (Ghahramani & Beal) which explains the model theory
    and has the parameter optimisation equations in the Appendix.

  o a jpg of the newer graphical model implemented in this code.

  o the VBMFA functions written in MATLAB, most of which have help lines.

DEMO:	load ueda_spiral; Y = Y(:,1:2:end);
	[Y ppp] = preprocess(Y);
	net = vbmfa(Y,1,0,0,10);
	
PLOT OPTION: after every accepted epoch, plots:
	a) 1sd ellipses of analysers,
	b) 3sd ellipses of analyser means (a distribution over each mean),
	c) history of F, and
	d) component mixing proportions.

The code should work, but is by no means perfect and is both redundant
and buggy in places. I shall fix it up in good time.

Please email with your comments/suggestions/bugs, but please check for
recent versions before doing so!

Enjoy

-Matt Beal


* Full means that we place distributions over all those parameters whos
cardinality increases with model complexity, and are as such integrated
out to form the marginal likelihood, or Evidence.

Undesirables:-

1) Certain combinations of death moves within epochs screw up the
component ordering. I haven't got around to fixing this.
2) There is a version of this code that *focuses* on only those components
that are in responsibility flux. This dramatically speeds up the search,
but is not needed to demonstrate the algorithm.
3) Better versions exist and will be posted as soon as I have time.