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复数域稀疏可分因子分析及局部场电位数据应用AI 解读

Complex-valued arrays arise in signal processing, where scientific interpretation depends on retaining amplitude and phase information. Existing covariance estimation methods either ignore the multiway organization of such data or rely on real-domain embeddings that do not directly exploit their complex structure. We develop sparse separable factor analysis (SSFA), a latent factor model for complex-valued arrays with a separable covariance structure across modes. Each…

高维高斯随机矩阵条件数与奇异值的矩界：应用与局限AI 解读

Spectral properties of Gram matrices are central to high dimensional asymptotic analyses of statistical estimators in regression and covariance estimation. These properties, in turn, depend critically on the extreme singular values and condition numbers of Gaussian random matrices. For many applications, sharp positive and negative moment bounds for these quantities are required to control expected prediction risk and related performance metrics. Although extensive work…

CoMET：面向高维张量的压缩贝叶斯混合效应模型AI 解读

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…