Sparse and low-rank estimation of time-varying Markov networks with alternating direction method of multipliers

Authors:
Jun-ichiro Hirayama;Aapo Hyvärinen;Shin Ishii
Affiliations:
Graduate School of Informatics, Kyoto University, Gokasho, Uji, Kyoto, Japan;Department of Mathematics and Statistics, Department of Computer Science and HIIT, University of Helsinki, Helsinki, Finland;Graduate School of Informatics, Kyoto University, Gokasho, Uji, Kyoto, Japan
Venue:
ICONIP'10 Proceedings of the 17th international conference on Neural information processing: theory and algorithms - Volume Part I
Year:
2010

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Abstract

Several authors have recently proposed sparse estimation techniques for time-varying Markov networks, in which both graph structures and model parameters may change with time. In this study, we extend a previous approach with a low-rank assumption on the matrix of parameter sequence, utilizing a recent technique of nuclear norm regularization. This can potentially improve the estimation performance particularly in such cases that the local smoothness assumed in previous studies do not really hold. Then, we derive a simple algorithm based on the alternating direction method of multipliers (ADMM) which can effectively utilize the separable structure of our convex minimization problem. With an artificially-generated dataset, its superior performance in structure learning is demonstrated.