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2020 Capturing between-tasks covariance and similarities using multivariate linear mixed models
Aviv Navon, Saharon Rosset
Electron. J. Statist. 14(2): 3821-3844 (2020). DOI: 10.1214/20-EJS1764


We consider the problem of predicting several response variables using the same set of explanatory variables. This setting naturally induces a group structure over the coefficient matrix, in which every explanatory variable corresponds to a set of related coefficients. Most of the existing methods that utilize this group formation assume that the similarities between related coefficients arise solely through a joint sparsity structure. In this paper, we propose a procedure for constructing multivariate regression models, that directly capture and model the within-group similarities, by employing a multivariate linear mixed model formulation, with a joint estimation of covariance matrices for coefficients and errors via penalized likelihood. Our approach, which we term MrRCE for Multivariate random Regression with Covariance Estimation, encourages structured similarity in parameters, in which coefficients for the same variable in related tasks share the same sign and similar magnitude. We illustrate the benefits of our approach in synthetic and real examples, and show that the proposed method outperforms natural competitors and alternative estimators under several model settings.


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Aviv Navon. Saharon Rosset. "Capturing between-tasks covariance and similarities using multivariate linear mixed models." Electron. J. Statist. 14 (2) 3821 - 3844, 2020.


Received: 1 November 2019; Published: 2020
First available in Project Euclid: 21 October 2020

zbMATH: 07270278
MathSciNet: MR4164865
Digital Object Identifier: 10.1214/20-EJS1764

Keywords: covariance selection , EM algorithm , multivariate regression , penalized likelihood , regularization methods , sparse precision matrix


Vol.14 • No. 2 • 2020
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