## Tree-dependent Component Analysis

Francis R. Bach

(Professor Michael I. Jordan)

Intel Corporation, (NSF) IIS-9988642, and (ONR/MURI) N00014-00-1-0637

We propose 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.

- [1]
- F. R. Bach and M. I. Jordan, "Tree-dependent Component Analysis,"
*Uncertainty in Artificial Intelligence Conf. Proc.,* Edmonton, Canada, August 2002.

More information (http://www.cs.berkeley.edu/~fbach) or

Send mail to the author : (fbach@cs.berkeley.edu)

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