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Minimax bounds for sparse pca with noisy high-dimensional data.
| Content Provider | CiteSeerX |
|---|---|
| Author | Birnbaum, Aharon Johnstone, Iain M. Nadler, Boaz Paul, Debashis |
| 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 l2 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. |
| File Format | |
| Journal | THE ANNALS OF STATISTICS |
| Journal | Submitted To The Annals Of Statistics |
| Access Restriction | Open |
| Subject Keyword | Two-stage Coordinate Selection Scheme Risk Point New Method Population Eigenvectors Independent Gaussian Observation Sample Size Increase High-dimensional Population Covariance Matrix Different Regime Minimax Risk L2 Loss Various Model Joint Limit |
| Content Type | Text |
| Resource Type | Article |
