Biao Cai

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.

The inference of gene co-expressions from microarray and RNA-sequencing data has led to rich insights on biological processes and disease mechanisms. However, the bulk samples analyzed in most studies are a mixture of different cell types. As a result, the inferred co-expressions are confounded by varying cell type compositions across samples and only offer an aggregated view of gene regulations that may be distinct across different cell types. 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. However, the high sequencing depth variations and measurement errors in scRNA-seq data present significant challenges in inferring cell-type-specific gene co-expressions, and these issues have not been adequately addressed in the existing methods. We propose a statistical approach, CS-CORE, for estimating and testing cell-type-specific co-expressions, built on a general expression-measurement model that explicitly accounts for sequencing depth variations and measurement errors in the observed single cell data. Systematic evaluations show that most existing methods suffer from inflated false positives and biased co-expression estimates and clustering analysis, whereas CS-CORE has appropriate false positive control, unbiased co-expression estimates, good statistical power and satisfactory performance in downstream co-expression analysis. When applied to analyze scRNA-seq data from postmortem brain samples from Alzheimer’s disease patients and controls and blood samples from COVID-19 patients and 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 other methods.