Tree-dependent component analysis

Authors:
Francis R. Bach;Michael I. Jordan
Affiliations:
Computer Science Division, University of California, Berkeley, CA;Computer Science Division and Department of Statistics, University of California, Berkeley, CA
Venue:
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Year:
2002

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Abstract

We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a tree-structured graphical model. Treating the problem as a semiparametric statistical problem, we show that the optimal transform is found by minimizing a contrast function based on mutual information, a function that directly extends the contrast function used for classical ICA. We provide two approximations of this contrast function, one using kernel density estimation, and another using kernel generalized variance. This tree-dependent component analysis framework leads naturally to an efficient general multivariate density estimation technique where only bivariate density estimation needs to be performed.