estimates the variational posterior distribution of a GMM on data using the variational EM algorithm (see references). A lower bound is calculated and monitored at each iteration. This posterior can be used for various purposes (e.g. MC proposal distribution). It can be transformed using extractSimpleModel, outputing a GMM.
Usage
varbayes(data, ncomp, thres = 0.1, maxit = NULL)
Arguments
data
matrix of row-elements.
ncomp
number of components in the posterior.
thres
threshold for lower bound variations between 2 iterations. Convergence is decided if this variation is below thres.
maxit
if NULL, the stopping criterion is related to thres. If not NULL, maxit iterations are performed.
Value
A list object, with the following items:
modelposterior variational distribution.
dataa copy of the data parameter.
nkcounts, for each iteration, of the population modeled by each Gaussian component.
agitationagitation measures (see Beal 2003 for explanation) for each iteration and Gaussian component.
boundlatest monitored bound value (convergence criterion maximized throughout the process).
The model item is structured in a list as follows:
alphahyperparameters influencing the active components in the posterior.
betahyperparameters regarding shaping of the Normal-Wishart posteriors.
nuhyperparameters regarding shaping of the Normal-Wishart posteriors.
meanhyperparameters regarding shaping of the Normal-Wishart posteriors.
wishhyperparameters regarding shaping of the Normal-Wishart posteriors.
References
Bishop, C. M. (2006) Pattern Recognition and Machine Learning, Chapter 10, Springer.
Beal, M. J. (2003) Variational Algorithms for approximate inference, PhD thesis, University of London.