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.

翻译：混合效应模型是分析聚类数据与重复测量数据的基础工具，但现有高维方法主要集中于向量型协变量的惩罚估计。该领域内的贝叶斯替代方案十分有限，目前尚无基于抽样的混合效应框架能够同时支持张量型固定效应与随机效应协变量，并保持计算可行性。本文针对具有标量响应和张量型协变量的高维重复测量数据，提出压缩混合效应张量（CoMET）模型。CoMET对随机效应协方差执行结构化的模态随机投影，得到低维协方差参数；该参数可采用简单的高斯先验设定，并能实现压缩随机效应的高效插补。在均值结构方面，CoMET利用低秩张量分解和边缘结构化马蹄先验来实现固定效应选择。这些设计选择导出了高效折叠吉布斯采样器，其计算复杂度随张量协变量维度近似线性增长。通过识别CoMET后验预测风险衰减至零的正则性条件，我们建立了高维理论保证。实证研究表明，在涉及面部表情预测和音乐情感建模的系列仿真实验与两个基准应用中，CoMET均优于惩罚估计类方法。