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ABSTRACT We address the challenge of estimating regression coefficients and selecting relevant predictors in the context of mixed linear regression in high dimensions, where the number of predictors greatly exceeds the sample size. Recent advancements in this field have centered on incorporating sparsity-inducing penalties into the expectation-maximization (EM) algorithm, which seeks to maximize the conditional likelihood of the response given the predictors. However, existing procedures often treat predictors as fixed or overlook their inherent variability. In this paper, we leverage the independence between the predictor and the latent indicator variable of mixtures to facilitate efficient computation and also achieve synergistic variable selection across all mixture components. We establish the non-asymptotic convergence rate of the proposed fast group-penalized EM estimator to the true regression parameters. The effectiveness of our method is demonstrated through extensive simulations and an application to the Cancer Cell Line Encyclopedia dataset for the prediction of anticancer drug sensitivity. 

The ratio of atmosphere-derived¹⁰Be to continent-derived⁹Be in marine sediments has been used to probe the long-term relationship between continental denudation and climate. However, its application is complicated by uncertainty in⁹Be transfer through the land-ocean interface. The riverine dissolved load alone is insufficient to close the marine⁹Be budget, largely due to substantial removal of riverine⁹Be to continental margin sediments. We focus on the ultimate fate of this latter Be. We present sediment pore-water Be profiles from diverse continental margin environments to quantify the diagenetic Be release to the ocean. Our results suggest that pore-water Be cycling is mainly controlled by particulate supply and Mn-Fe cycling, leading to higher benthic fluxes on shelves. Benthic fluxes may help close the⁹Be budget and are at least comparable to, or higher (~2-fold) than, the riverine dissolved input. These observations demand a revised model framework, which considers the potentially dominant benthic source, to robustly interpret marine Be isotopic records. 

Abstract In the form of multidimensional arrays, tensor data have become increasingly prevalent in modern scientific studies and biomedical applications such as computational biology, brain imaging analysis, and process monitoring system. These data are intrinsically heterogeneous with complex dependencies and structure. Therefore, ad‐hoc dimension reduction methods on tensor data may lack statistical efficiency and can obscure essential findings. Model‐based clustering is a cornerstone of multivariate statistics and unsupervised learning; however, existing methods and algorithms are not designed for tensor‐variate samples. In this article, we propose a tensor envelope mixture model (TEMM) for simultaneous clustering and multiway dimension reduction of tensor data. TEMM incorporates tensor‐structure‐preserving dimension reduction into mixture modeling and drastically reduces the number of free parameters and estimative variability. An expectation‐maximization‐type algorithm is developed to obtain likelihood‐based estimators of the cluster means and covariances, which are jointly parameterized and constrained onto a series of lower dimensional subspaces known as the tensor envelopes. We demonstrate the encouraging empirical performance of the proposed method in extensive simulation studies and a real data application in comparison with existing vector and tensor clustering methods.