@MISC{Amari_superefficiencyin, author = {Shun-ichi Amari}, title = {Superefficiency in Blind Source Separation}, year = {} }

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Abstract

Blind source separation extracts independent component signals from their mixtures without knowing the mixing coefficients nor the probability distributions of source signals. It is known that some algorithms work surprisingly well. The present paper elucidates the superefficiency of algorithms based on the statistical analysis. It is in general known from the asymptotic theory of statistical analysis that the covariance of any two extracted independent signals converges to 0 in the order of 1=t in the case of statistical estimation by using t examples. In the case of on-line learning, the theory of on-line dynamics shows that the covariances converge to 0 in the order of j when the learning rate j is fixed to be a small constant. In contrast with the above general properties, the surprising superefficiency holds in blind source separation under a certain conditions. The superefficiency implies that the covariance decreases in the order of 1=t 2 or of j 2 . The present paper uses t...