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ABSTRACT This work considers estimation and forecasting in a multivariate, possibly high‐dimensional count time series model constructed from a transformation of a latent Gaussian dynamic factor series. The estimation of the latent model parameters is based on second‐order properties of the count and underlying Gaussian time series, yielding estimators of the underlying covariance matrices for which standard principal component analysis applies. Theoretical consistency results are established for the proposed estimation, building on certain concentration results for the models of the type considered. They also involve the memory of the latent Gaussian process, quantified through a spectral gap, shown to be suitably bounded as the model dimension increases, which is of independent interest. In addition, novel cross‐validation schemes are suggested for model selection. The forecasting is carried out through a particle‐based sequential Monte Carlo, leveraging Kalman filtering techniques. A simulation study and an application are also considered. 

ABSTRACT This work introduces a novel framework for dynamic factor model‐based group‐level analysis of multiple subjects time‐series data, called GRoup Integrative DYnamic factor (GRIDY) models. The framework identifies and characterizes intersubject similarities and differences between two predetermined groups by considering a combination of group spatial information and individual temporal dynamics. Furthermore, it enables the identification of intrasubject similarities and differences over time by employing different model configurations for each subject. Methodologically, the framework combines a novel principal angle‐based rank selection algorithm and a noniterative integrative analysis framework. Inspired by simultaneous component analysis, this approach also reconstructs identifiable latent factor series with flexible covariance structures. The performance of the GRIDY models is evaluated through simulations conducted under various scenarios. An application is also presented to compare resting‐state functional MRI data collected from multiple subjects in autism spectrum disorder and control groups. 

Abstract In recommender systems, users rate items, and are subsequently served other product recommendations based on these ratings. Even though users usually rate a tiny percentage of the available items, the system tries to estimate unobserved preferences by finding similarities across users and across items. In this work, we treat the observed ratings data as partially observed, dense, weighted, bipartite networks. For a class of systems without outside information, we adapt an approach developed for dense, weighted networks to account for unobserved edges and the bipartite nature of the problem. The approach begins with clustering both users and items into communities, and locally estimates the patterns of ratings within each subnetwork induced by restricting attention to one community of users and one community of items community. The local fitting procedure relies on estimating local sociability parameters for every user and item, and selecting the function that determines the degree correction contours which best models the underlying data. We compare the performance of our proposed approach to existing methods on a simulated data set, as well as on a data set of joke ratings, examining model performance in both cases at differing levels of sparsity. On the joke ratings data set, our proposed model performs better than existing alternatives in relatively sparse settings, though other approaches achieve better results when more data is available. Collectively, the results indicate that despite struggling to pick up subtler signals, the proposed approach’s recovery of large scale, coarse patterns may still be useful in practical settings where high sparsity is typical. 

Clustering is a fundamental tool for exploratory data analysis. One central problem in clustering is deciding if the clusters discovered by clustering methods are reliable as opposed to being artifacts of natural sampling variation. Statistical significance of clustering (SigClust) is a recently developed cluster evaluation tool for high-dimension, low-sample size data. Despite its successful application to many scientific problems, there are cases where the original SigClust may not work well. Furthermore, for specific applications, researchers may not have access to the original data and only have the dissimilarity matrix. In this case, clustering is still a valuable exploratory tool, but the original SigClust is not applicable. To address these issues, we propose a new SigClust method using multidimensional scaling (MDS). The underlying idea behind MDS-based SigClust is that one can achieve low-dimensional representations of the original data via MDS using only the dissimilarity matrix and then apply SigClust on the low-dimensional MDS space. The proposed MDS-based SigClust can circumvent the challenge of parameter estimation of the original method in high-dimensional spaces while keeping the essential clustering structure in the MDS space. Both simulations and real data applications demonstrate that the proposed method works remarkably well for assessing the statistical significance of clustering. Supplementary materials for this article are available online.