Complexity Theoretic Lower Bounds for Sparse Principal Component Detection
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.
Cite
Text
Berthet and Rigollet. "Complexity Theoretic Lower Bounds for Sparse Principal Component Detection." Annual Conference on Computational Learning Theory, 2013.Markdown
[Berthet and Rigollet. "Complexity Theoretic Lower Bounds for Sparse Principal Component Detection." Annual Conference on Computational Learning Theory, 2013.](https://mlanthology.org/colt/2013/berthet2013colt-complexity/)BibTeX
@inproceedings{berthet2013colt-complexity,
title = {{Complexity Theoretic Lower Bounds for Sparse Principal Component Detection}},
author = {Berthet, Quentin and Rigollet, Philippe},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2013},
pages = {1046-1066},
url = {https://mlanthology.org/colt/2013/berthet2013colt-complexity/}
}