Subexponential-Time Algorithms for Sparse PCA

We study the computational cost of recovering a unit-norm sparse principal component x ∈ R n planted in a random matrix, in either the Wigner or Wishart spiked model (observing either W + λ x x ⊤ with W drawn from the Gaussian orthogonal ensemble, or N independent samples from N ( 0 , I n + β x x ⊤...

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Bibliographic Details
Published in:	Foundations of computational mathematics Vol. 24; no. 3; pp. 865 - 914
Main Authors:	Ding, Yunzi, Kunisky, Dmitriy, Wein, Alexander S., Bandeira, Afonso S.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.06.2024 Springer Nature B.V
Subjects:	Algorithms Applications of Mathematics Computational efficiency Computer Science Economics Likelihood ratio Linear and Multilinear Algebras Math Applications in Computer Science Mathematics Mathematics and Statistics Matrix Theory Numerical Analysis Polynomials Principal components analysis Recovery Search algorithms Signal to noise ratio Tradeoffs Low-degree likelihood ratio Sparse PCA Computational complexity 62F03 68Q87 68Q17
ISSN:	1615-3375, 1615-3383
Online Access:	Get full text
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