Regularized Parameter Estimation in Mixed Model Trace Regression

Ian Hultman; Sanvesh Srivastava

doi:10.48550/arxiv.2503.13782

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Regularized Parameter Estimation in Mixed Model Trace Regression

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Regularized Parameter Estimation in Mixed Model Trace Regression

Ian Hultman and Sanvesh Srivastava

ArXiV.org

Cornell University

03/17/2025

DOI: 10.48550/arxiv.2503.13782

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https://doi.org/10.48550/arxiv.2503.13782View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We introduce mixed model trace regression (MMTR), a mixed model linear regression extension for scalar responses and high-dimensional matrix-valued covariates. MMTR's fixed effects component is equivalent to trace regression, with an element-wise lasso penalty imposed on the regression coefficients matrix to facilitate the estimation of a sparse mean parameter. MMTR's key innovation lies in modeling the covariance structure of matrix-variate random effects as a Kronecker product of low-rank row and column covariance matrices, enabling sparse estimation of the covariance parameter through low-rank constraints. We establish identifiability conditions for the estimation of row and column covariance matrices and use them for rank selection by applying group lasso regularization on the columns of their respective Cholesky factors. We develop an Expectation-Maximization (EM) algorithm extension for numerically stable parameter estimation in high-dimensional applications. MMTR achieves estimation accuracy comparable to leading regularized quasi-likelihood competitors across diverse simulation studies and attains the lowest mean square prediction error compared to its competitors on a publicly available image dataset.

Statistics - Computation

Statistics - Methodology

Details

Title: Subtitle: Regularized Parameter Estimation in Mixed Model Trace Regression
Creators: Ian Hultman - University of Iowa
Sanvesh Srivastava - University of Iowa
Resource Type: Preprint
Publication Details: ArXiV.org
DOI: 10.48550/arxiv.2503.13782
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 03/17/2025
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9984801841202771

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