Open Access
Translator Disclaimer
June 2013 Minimax bounds for sparse PCA with noisy high-dimensional data
Aharon Birnbaum, Iain M. Johnstone, Boaz Nadler, Debashis Paul
Ann. Statist. 41(3): 1055-1084 (June 2013). DOI: 10.1214/12-AOS1014

Abstract

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.

Citation

Download Citation

Aharon Birnbaum. Iain M. Johnstone. Boaz Nadler. Debashis Paul. "Minimax bounds for sparse PCA with noisy high-dimensional data." Ann. Statist. 41 (3) 1055 - 1084, June 2013. https://doi.org/10.1214/12-AOS1014

Information

Published: June 2013
First available in Project Euclid: 13 June 2013

zbMATH: 1292.62071
MathSciNet: MR3113803
Digital Object Identifier: 10.1214/12-AOS1014

Subjects:
Primary: 62G20
Secondary: 62H25

Keywords: High-dimensional data , minimax risk , Principal Component Analysis , Sparsity , spiked covariance model

Rights: Copyright © 2013 Institute of Mathematical Statistics

JOURNAL ARTICLE
30 PAGES


SHARE
Vol.41 • No. 3 • June 2013
Back to Top