Optimal detection of sparse principal components in high dimension

Details Optimal detection of sparse principal components in high dimension Optimal detection of sparse principal components in high dimension

2012-02-23

arxiv.org/abs/1202.5070v1

Mathematics

Statistics Theory

Scientific paper

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to be NP-complete in general and we describe a computationally efficient alternative test using convex relaxations. Our relaxation is also proved to detect sparse principal components at near optimal detection levels and performs very well on simulated datasets.

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