Minimax bounds for sparse PCA with noisy high-dimensional data

Details Minimax bounds for sparse PCA with noisy high-dimensional data Minimax bounds for sparse PCA with noisy high-dimensional data

2012-03-05

arxiv.org/abs/1203.0967v1

Mathematics

Statistics Theory

1 figure

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Minimax bounds for sparse PCA with noisy high-dimensional data does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Minimax bounds for sparse PCA with noisy high-dimensional data, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimax bounds for sparse PCA with noisy high-dimensional data will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-133789