Generalized Co-sparse Factor Regression

Aditya Mishra; Dipak K. Dey; Yong Chen; Kun Chen

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arXiv · 2010.08134

Generalized Co-sparse Factor Regression

Aditya Mishra·Dipak K. Dey·Yong Chen·Kun Chen

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Abstract

Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements, binary indicators, and counts, and the observations may also be incomplete. Building upon the recent advances in mixed-outcome modeling and sparse matrix factorization, generalized co-sparse factor regression (GOFAR) is proposed, which utilizes the flexible vector generalized linear model framework and encodes the outcome dependency through a sparse singular value decomposition (SSVD) of the integrated natural parameter matrix. To avoid the estimation of the notoriously difficult joint SSVD, GOFAR proposes both sequential and parallel unit-rank estimation procedures. By combining the ideas of alternating convex search and majorization-minimization, an efficient algorithm with guaranteed convergence is developed to solve the sparse unit-rank problem and implemented in the R package gofar. Extensive simulation studies and two real-world applications demonstrate the effectiveness of the proposed approach.

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Aditya Mishra, Dipak K. Dey, Yong Chen, Kun Chen. 2020-10-16. Generalized Co-sparse Factor Regression. https://arxiv.org/abs/2010.08134

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