MINIMAX BOUNDS FOR SPARSE PCA WITH NOISY HIGH-DIMENSIONAL DATA

被引：93

作者：

Birnbaum, Aharon ^{[1
]}

Johnstone, Iain M. ^{[2
]}

Nadler, Boaz ^{[3
]}

Paul, Debashis ^{[4
]}

机构：

[1] Hebrew Univ Jerusalem, Jerusalem 91904, Israel

[2] Stanford Univ, Dept Stat, Stanford, CA 94305 USA

[3] Weizmann Inst Sci, Dept Comp Sci & Appl Math, Rehovot 76100, Israel

[4] Univ Calif Davis, Dept Stat, Davis, CA 95616 USA

来源：

ANNALS OF STATISTICS | 2013年 / 41卷 / 03期

基金：

美国国家科学基金会;

关键词：

Minimax risk; high-dimensional data; principal component analysis; sparsity; spiked covariance model; PRINCIPAL-COMPONENTS-ANALYSIS; CONSISTENCY; RATES;

D O I：

10.1214/12-AOS1014

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the l(2) loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the risk points to the existence of different regimes of sparsity of the eigenvectors. We also propose a new method for estimating the eigenvectors by a two-stage coordinate selection scheme.

引用

页码：1055 / 1084

页数：30

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