PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

The kernel mutual information
Arthur Gretton, Ralf Herbrich and Alex Smola
(2003) Technical Report. MPI for Biological Cybernetics Technical Report, Tuebingen,Germany.

Abstract

We introduce two new functions, the kernel covariance (KC) and the kernel mutual information (KMI), to measure the degree of independence of several continuous random variables. The former is guaranteed to be zero if and only if the random variables are pairwise independent; the latter shares this property, and is in addition an approximate upper bound on the mutual information, as measured near independence, and is based on a kernel density estimate. We show that Bach and Jordan's kernel generalised variance (KGV) is also an upper bound on the same kernel density estimate, but is looser. Finally, we suggest that the addition of a regularising term in the KGV causes it to approach the KMI, which motivates the introduction of this regularisation. The performance of the KC and KMI is verified in the context of instantaneous independent component analysis (ICA), by recovering both artificial and real (musical) signals following linear mixing.

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EPrint Type:Monograph (Technical Report)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:399
Deposited By:Arthur Gretton
Deposited On:19 December 2004