Optimal detection of sparse principal components in high dimension
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In this paper, a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix is performed, based on a sparse eigenvalue statistic.Abstract:
We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to be NP-complete in general, and we describe a computationally efficient alternative test using convex relaxations. Our relaxation is also proved to detect sparse principal components at near optimal detection levels, and it performs well on simulated datasets. Moreover, using polynomial time reductions from theoretical computer science, we bring significant evidence that our results cannot be improved, thus revealing an inherent trade off between statistical and computational performance.read more
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References
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Stephen Boyd,Lieven Vandenberghe +1 more
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Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays.
Uri Alon,Naama Barkai,Daniel A. Notterman,Kurt C. Gish,S. Ybarra,David H. Mack,A. J. Levine,A. J. Levine +7 more
TL;DR: In this paper, a two-way clustering algorithm was applied to both the genes and the tissues, revealing broad coherent patterns that suggest a high degree of organization underlying gene expression in these tissues.
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Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
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