A quasi-stochastic gradient algorithm for variance-dependent component analysis

Authors:
Aapo Hyvärinen;Shohei Shimizu
Affiliations:
Helsinki Institute for Information Technology, University of Helsinki, Finland;Helsinki Institute for Information Technology, University of Helsinki, Finland
Venue:
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part II
Year:
2006

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Abstract

We discuss the blind source separation problem where the sources are not independent but are dependent only through their variances. Some estimation methods have been proposed on this line. However, most of them require some additional assumptions: a parametric model for their dependencies or a temporal structure of the sources, for example. In previous work, we have proposed a generalized least squares approach using fourth-order moments to the blind source separation problem in the general case where those additional assumptions do not hold. In this article, we develop a simple optimization algorithm for the least squares approach, or a quasi-stochastic gradient algorithm. The new algorithm is able to estimate variance-dependent components even when the number of variables is large and the number of moments is computationally prohibitive.