Efficient parallel computation of the stochastic MV-PURE estimator by the hybrid steepest descent method

Authors:
Tomasz Piotrowski;Isao Yamada
Affiliations:
Dept. of Informatics, Nicolaus Copernicus University, Torunń, Poland;Dept. of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, Japan
Venue:
ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part II
Year:
2012

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Abstract

In this paper we consider the problem of efficient computation of the stochastic MV-PURE estimator which is a reduced-rank estimator designed for robust linear estimation in ill-conditioned inverse problems. Our motivation for this result stems from the fact that the reduced-rank estimation by the stochastic MV-PURE estimator, while avoiding the problem of regularization parameter selection appearing in a common regularization technique used in inverse problems and machine learning, presents computational challenge due to nonconvexity induced by the rank constraint. To combat this problem, we propose a recursive scheme for computation of the general form of the stochastic MV-PURE estimator which does not require any matrix inversion and utilize the inherently parallel hybrid steepest descent method. We verify efficiency of the proposed scheme in numerical simulations.