Sreya Sarkar | Searcharxiv

arXiv2026

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

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.

stat.ME↗

arXiv2025

Bayesian Compressed Mixed-Effects Models

Penalized likelihood and quasi-likelihood methods dominate inference in high-dimensional linear mixed-effects models. Sampling-based Bayesian inference is less explored due to the computational bottlenecks introduced by the random effects covariance matrix. To address this gap, we propose the compressed mixed-effects (CME) model, which defines a quasi-likelihood using low-dimensional covariance parameters obtained via random projections of the random effects covariance. This dimension reduction, combined with a global-local shrinkage prior on the fixed effects, yields an efficient collapsed Gibbs sampler for prediction and fixed effects selection. Theoretically, when the compression dimension grows slowly relative to the number of fixed effects and observations, the Bayes risk for prediction is asymptotically negligible, ensuring accurate prediction using the CME model. Empirically, the CME model outperforms existing approaches in terms of predictive accuracy, interval coverage, and fixed-effects selection across varied simulation settings and a real-world dataset.

stat.ME↗