Measures of Statistical Dependence
A number of important problems in signal processing depend on measures of statistical dependence. For instance, this dependence is minimised in the context of instantaneous ICA, in which linearly mixed signals are separated using their (assumed) pairwise independence from each other. A number of methods have been proposed to measure this dependence, however they generally assume a particular parametric model for the densities generating the observations. Recent work suggests that kernel methods may be used to find estimates that adapt according to the signals they compare. These methods are currently being refined, both to yeild greater accuracy, and to permit the use of the signal properties over time in improving signal separability. In addition, these methods can be applied in cases where the statistical dependence between observations must be maximised, which is true for certain classes of clustering algorithms.
Author: Arthur Gretton, Max Planck Institute for Biological Cybernetics