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Variational Bayesian Learning of ICA with Missing Data

kwchan{at}salk.edu, Computational Neurobiology Laboratory, Salk Institute, La Jolla, CA 92037, U.S.A.

Te-Won Lee

tewon{at}salk.edu, Institute for Neural Computation, University of California at San Diego, La Jolla, CA 92093, U.S.A.

Terrence J. Sejnowski

terry{at}salk.edu, Computational Neurobiology Laboratory, Salk Institute, La Jolla, CA 92037, U.S.A., and Department of Biology, University of California at San Diego, La Jolla, CA 92093, U.S.A.

Missing data are common in real-world data sets and are a problem for many estimation techniques. We have developed a variational Bayesian method to perform independent component analysis (ICA) on highdimensional data containing missing entries. Missing data are handled naturally in the Bayesian framework by integrating the generative density model. Modeling the distributions of the independent sources with mixture of gaussians allows sources to be estimated with different kurtosis and skewness. Unlike the maximum likelihood approach, the variational Bayesian method automatically determines the dimensionality of the data and yields an accurate density model for the observed data without overfitting problems. The technique is also extended to the clusters of ICA and supervised classification framework.

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