CoMET: A Compressed Bayesian Mixed-Effects Model for High-Dimensional Tensors

Sreya Sarkar; Kshitij Khare; Sanvesh Srivastava

doi:10.48550/arxiv.2602.19236

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CoMET: A Compressed Bayesian Mixed-Effects Model for High-Dimensional Tensors

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CoMET: A Compressed Bayesian Mixed-Effects Model for High-Dimensional Tensors

Sreya Sarkar, Kshitij Khare and Sanvesh Srivastava

ArXiv.org

Cornell University

02/22/2026

DOI: 10.48550/arxiv.2602.19236

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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

Mixed-effects models are fundamental tools for analyzing clustered and repeated-measures data, but existing high-dimensional methods largely focus on penalized estimation with vector-valued covariates. Bayesian alternatives in this regime are limited, with no sampling-based mixed-effects framework that supports tensor-valued fixed- and random-effects covariates while remaining computationally tractable. We propose the Compressed Mixed-Effects Tensor (CoMET) model for high-dimensional repeated-measures data with scalar responses and tensor-valued covariates. CoMET performs structured, mode-wise random projection of the random-effects covariance, yielding a low-dimensional covariance parameter that admits simple Gaussian prior specification and enables efficient imputation of compressed random-effects. For the mean structure, CoMET leverages a low-rank tensor decomposition and margin-structured Horseshoe priors to enable fixed-effects selection. These design choices lead to an efficient collapsed Gibbs sampler whose computational complexity grows approximately linearly with the tensor covariate dimensions. We establish high-dimensional theoretical guarantees by identifying regularity conditions under which CoMET's posterior predictive risk decays to zero. Empirically, CoMET outperforms penalized competitors across a range of simulation studies and two benchmark applications involving facial-expression prediction and music emotion modeling.

Statistics - Methodology

Details

Title: Subtitle: CoMET: A Compressed Bayesian Mixed-Effects Model for High-Dimensional Tensors
Creators: Sreya Sarkar
Kshitij Khare
Sanvesh Srivastava
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2602.19236
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 02/22/2026
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9985139469102771

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