Minimax estimation in sparse canonical correlation analysis
نویسندگان
چکیده
منابع مشابه
Minimax Estimation in Sparse Canonical Correlation Analysis
Canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables. This paper considers the problem of estimating the leading canonical correlation directions in high dimensional settings. Recently, under the assumption that the leading canonical correlation directions are sparse, various procedures have been proposed for...
متن کاملSupplement to “minimax Estimation in Sparse Canonical Correlation Analysis”
In this appendix, we prove Theorem 4 and Lemmas 7 – 12 in order. A.1. Proof of Theorem 4. We first need a lemma for perturbation bound of square root matrices. Lemma 16. Let A, B be positive semi-definite matrices, and then for any unitarily invariant norm ï¿¿·ï¿¿, ï¿¿A 1/2 − B 1/2 ï¿¿ ≤ 1 σ min (A 1/2) + σ min (B 1/2) ï¿¿A − Bï¿¿. Proof. The proof essentially follows the idea of [27]. Let D = ...
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Given two data matrices X and Y , Sparse canonical correlation analysis (SCCA) is to seek two sparse canonical vectors u and v to maximize the correlation between Xu and Y v. However, classical and sparse CCA models consider the contribution of all the samples of data matrices and thus cannot identify an underlying specific subset of samples. To this end, we propose a novel Sparse weighted cano...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2015
ISSN: 0090-5364
DOI: 10.1214/15-aos1332