Decision Sciences Seminar
Friday April 12, 2013
11:00AM - 12:30PM
Philippe Rigollet Princeton University
The statistical price to pay for computational efficiency in sparse PCA
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 polynomial time.