$\ell_1$-norm constrained multi-block sparse canonical correlation analysis via proximal gradient descent

• URL: http://arxiv.org/abs/2201.05289v1
• Date: Fri, 14 Jan 2022 03:35:01 GMT
• Title: $\ell_1$-norm constrained multi-block sparse canonical correlation analysis via proximal gradient descent
• Authors: Leying Guan
• Abstract summary: We propose a proximal gradient descent algorithm to solve the multi-block CCA problem. We show that the resulting estimate is rate-optimal under suitable assumptions. We also describe an easy-to-implement deflation procedure to estimate multiple eigenvectors sequentially.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multi-block CCA constructs linear relationships explaining coherent variations across multiple blocks of data. We view the multi-block CCA problem as finding leading generalized eigenvectors and propose to solve it via a proximal gradient descent algorithm with $\ell_1$ constraint for high dimensional data. In particular, we use a decaying sequence of constraints over proximal iterations, and show that the resulting estimate is rate-optimal under suitable assumptions. Although several previous works have demonstrated such optimality for the $\ell_0$ constrained problem using iterative approaches, the same level of theoretical understanding for the $\ell_1$ constrained formulation is still lacking. We also describe an easy-to-implement deflation procedure to estimate multiple eigenvectors sequentially. We compare our proposals to several existing methods whose implementations are available on R CRAN, and the proposed methods show competitive performances in both simulations and a real data example.

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