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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.
