Estimation of low-rank covariance function

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Koltchinskii, V.¹  Lounici, K.¹  Tsybakov, A. B.² 

[1] Georgia Inst Technol, 686 Cherry St, Atlanta, GA 30332 USA

[2] CREST ENSAE, Lab Stat, 3 Ave P Larousse, F-92240 Malakoff, France

关键词: Gaussian process;    Low rank covariance function;    Nuclear norm;    Empirical risk minimization;    Minimax lower bounds;    Adaptationf;   

DOI  :  10.1016/j.spa.2016.04.006

来源: Elsevier

【 摘 要 】

We consider the problem of estimating a low rank covariance function K (t, u) of a Gaussian process S(t), t epsilon [0, 1] based on n i.i.d. copies of S observed in a white noise. We suggest a new estimation procedure adapting simultaneously to the low rank structure and the smoothness of the covariance function. The new procedure is based on nuclear norm penalization and exhibits superior performances as compared to the sample covariance function by a polynomial factor in the sample size n. Other results include a minimax lower bound for estimation of low-rank covariance functions showing that our procedure is optimal as well as a scheme to estimate the unknown noise variance of the Gaussian process. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free