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Sparse CCA via Precision Adjusted Iterative Thresholding

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arxiv 1311.6186 v1 pith:2WRJS5LF submitted 2013-11-24 math.ST stat.MEstat.MLstat.TH

Mengjie Chen , Chao Gao , Zhao Ren , Harrison H. Zhou This is my paper · ORCID
classification math.STstat.MEstat.MLstat.TH
keywords sparsecancerprocedureanalysisappliedbeenbreastcanonical
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Sparse Canonical Correlation Analysis (CCA) has received considerable attention in high-dimensional data analysis to study the relationship between two sets of random variables. However, there has been remarkably little theoretical statistical foundation on sparse CCA in high-dimensional settings despite active methodological and applied research activities. In this paper, we introduce an elementary sufficient and necessary characterization such that the solution of CCA is indeed sparse, propose a computationally efficient procedure, called CAPIT, to estimate the canonical directions, and show that the procedure is rate-optimal under various assumptions on nuisance parameters. The procedure is applied to a breast cancer dataset from The Cancer Genome Atlas project. We identify methylation probes that are associated with genes, which have been previously characterized as prognosis signatures of the metastasis of breast cancer.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Efficient Canonical Correlation Analysis with Sparsity

    stat.ME 2025-07 conditional novelty 6.0 of 10

    ECCAR reformulates sparse CCA as a Lasso-style regression on the identity matrix, yielding fast computation with proved error bounds and one-sided support recovery.

  2. Stochastic optimization over expectation-formulated generalized Stiefel manifold

    math.OC 2024-12 conditional novelty 6.0 of 10

    A new sixth-order penalty function makes stochastic optimization over expectation-formulated generalized Stiefel manifolds equivalent to unconstrained optimization, enabling stochastic gradient methods with O(epsilon^...

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