Complexity Theoretic Lower Bounds for Sparse Principal Component Detection

author: Quentin Berthet, Department of Operations Research and Financial Engineering, Princeton University
published: Aug. 9, 2013,   recorded: June 2013,   views: 472
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Description

In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can detect and we propose a computationally efficient method based on semidefinite programming. We also prove that the statistical performance of this test cannot be strictly improved by any computationally efficient method. Our results can be viewed as complexity theoretic lower bounds conditionally on the assumptions that some instances of the planted clique problem cannot be solved in randomized polynomial time.

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Comment1 Philippe Buzenet, August 12, 2013 at 7:01 p.m.:

Bravo , the problem has been masterly "harnessed" .

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