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Tackling High-Dimensional Tensor Clustering In the paper “Jointly Modeling and Clustering Tensors in High Dimensions,” Cai, Zhang, and Sun address the challenge of jointly modeling and clustering tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. The proposed mixture model exploits the intrinsic structures of tensor data. The authors develop a computationally efficient high-dimensional expectation conditional maximization (HECM) algorithm and show that the HECM iterates, with an appropriate initialization, converge geometrically to a neighborhood that is within statistical precision of the true parameter. The theoretical analysis is nontrivial because of the dual nonconvexity arising from both the expectation maximization-type estimation and the nonconvex objective function in the M step. They also study the convergence rate of the algorithm when the number of clusters is overspecified and when the signal-to-noise ratio diminishes with sample size. The efficacy of the proposed method is demonstrated through numerical experiments and a real-world medical data application. 

Abstract The advancement of single cell RNA-sequencing (scRNA-seq) technology has enabled the direct inference of co-expressions in specific cell types, facilitating our understanding of cell-type-specific biological functions. For this task, the high sequencing depth variations and measurement errors in scRNA-seq data present two significant challenges, and they have not been adequately addressed by existing methods. We propose a statistical approach, CS-CORE, for estimating and testing cell-type-specific co-expressions, that explicitly models sequencing depth variations and measurement errors in scRNA-seq data. Systematic evaluations show that most existing methods suffered from inflated false positives as well as biased co-expression estimates and clustering analysis, whereas CS-CORE gave accurate estimates in these experiments. When applied to scRNA-seq data from postmortem brain samples from Alzheimer’s disease patients/controls and blood samples from COVID-19 patients/controls, CS-CORE identified cell-type-specific co-expressions and differential co-expressions that were more reproducible and/or more enriched for relevant biological pathways than those inferred from existing methods.