Cauchy noise loss for stochastic optimization of random matrix models via free deterministic equivalents

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:483

Article

Hayase, Tomohiro¹ 

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan

关键词: Random matrix theory;    Free probability theory;    Stochastic optimization;    Rank estimation;    Dimensionality recovery;   

DOI  :  10.1016/j.jmaa.2019.123597

来源: Elsevier

【 摘 要 】

For random matrix models, the parameter estimation based on the traditional likelihood functions is not straightforward in particular when we have only one sample matrix. We introduce a new parameter optimization method for random matrix models which works even in such a case. The method is based on the spectral distribution instead of the traditional likelihood. In the method, the Cauchy noise has an essential role because the free deterministic equivalent, which is a tool in free probability theory, allows us to approximate the spectral distribution perturbed by Cauchy noises by a smooth and accessible density function. Moreover, we study an asymptotic property of determination gap, which has a similar role as generalization gap. Besides, we propose a new dimensionality recovery method for the signal-plusnoise model, and experimentally demonstrate that it recovers the rank of the signal part even if the true rank is not small. It is a simultaneous rank selection and parameter estimation procedure. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free