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Complexity theoretic lower bounds for sparse principal component detection

Author(s): Berthet, Quentin; Rigollet, Philippe

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Abstract: 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. © 2013 Q. Berthet & P. Rigollet.
Publication Date: 1-Jan-2013
Citation: Berthet, Q, Rigollet, P. (2013). Complexity theoretic lower bounds for sparse principal component detection. Journal of Machine Learning Research, 30 (1046 - 1066). Retrieved from
ISSN: 1532-4435
EISSN: 1533-7928
Pages: 1046 - 1066
Type of Material: Journal Article
Journal/Proceeding Title: Journal of Machine Learning Research
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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