Generalized Co-sparse Factor Regression

TL;DR

The paper introduces GOFAR, a flexible multivariate regression method for mixed outcome types that uses sparse matrix factorization and efficient algorithms, demonstrated through simulations and real data.

Contribution

GOFAR advances multivariate regression by integrating mixed outcomes with sparse singular value decomposition and efficient estimation procedures.

Findings

Effective in modeling mixed outcome data

Demonstrates superior performance in simulations

Successfully applied to real-world datasets

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.