Sparse PCA: Optimal rates and adaptive estimation
نویسندگان
چکیده
منابع مشابه
Sparse PCA: Optimal Rates and Adaptive Estimation
Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional setting. Under mild technical conditions, we first establish the optimal rates of convergence for estimating the principal subspace which are sharp with respect to...
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Principal components analysis (PCA) is the optimal linear encoder of data. Sparse linear encoders (e.g., sparse PCA) produce more interpretable features that can promote better generalization. (i) Given a level of sparsity, what is the best approximation to PCA? (ii) Are there efficient algorithms which can achieve this optimal combinatorial tradeoff? We answer both questions by providing the f...
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We state below two results that we use frequently in our proofs. The first is well-known consequence of the CS decomposition. It relates the canonical angles between subspaces to the singular values of products and differences of their corresponding projection matrices.
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2013
ISSN: 0090-5364
DOI: 10.1214/13-aos1178