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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENT SEMINAR}
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\centerline{4:15 p.m., Tuesday, March 12, 2002}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Micheal Jordan}
\centerline{\sl UC Berkeley}
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\centerline{\bf Kernel Independent Component Analysis}
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Independent component analysis (ICA) refers to a class of latent variable
models in which a set of "sources" must be recovered from an unknown
set of linear mixtures of these sources.  The problem is reminiscent
of factor analysis, but whereas factor analysis assumes Gaussian latent
variables, ICA is meaningful only for non-Gaussian latent variables;
moreover, the distribution of the latent variables is assumed to be
unknown.  The problem is thus a semiparametric problem---we wish to estimate
the mixing matrix under any (non-Gaussian) distribution for the sources.

We present a new class of algorithms for ICA which use contrast functions
based on canonical correlations in a reproducing kernel Hilbert space
(RKHS).  On the one hand, we show that our contrast functions are related
to mutual information and have desirable mathematical properties as
measures of statistical dependence.  On the other hand, building on
recent developments in RKHS methods, we show that these criteria
and their derivatives can be computed efficiently.  Minimizing these
criteria leads to flexible and robust algorithms for ICA.  We illustrate
with simulations involving a wide variety of source distributions,
showing that our algorithms outperform presently known algorithms.

[Joint work with Francis Bach].

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