Many problems in high-dimensional data analysis can be cast
in terms of assessments of mutual independence or conditional
independence among subsets of measured variables or transforms
of measured variables. We present a nonparametric characterization
of mutual independence and conditional independence using operators
on reproducing kernel Hilbert spaces. We show how these operators
can be estimated from data and how they can be used in problems
such as independent component analysis, tree-dependent component analysis, and dimension reduction for regression and classification.
[Joint work with Francis Bach and Kenji Fukumizu].
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