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:
model
posterior variational distribution.
data
a copy of the data parameter.
nk
counts, for each iteration, of the population modeled by each Gaussian component.
agitation
agitation measures (see Beal 2003 for explanation) for each iteration and Gaussian component.
bound
latest monitored bound value (convergence criterion maximized throughout the process).
The model item is structured in a list as follows:
alpha
hyperparameters influencing the active components in the posterior.
beta
hyperparameters regarding shaping of the Normal-Wishart posteriors.
nu
hyperparameters regarding shaping of the Normal-Wishart posteriors.
mean
hyperparameters regarding shaping of the Normal-Wishart posteriors.
wish
hyperparameters 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.