This project has innovated a range of new methodologies, theories, and scalable computational tools to advance statistical learning with multivariate and multi-view data. Multi-view data, or the measuring of several distinct yet interrelated sets of characteristics pertaining to a single set of subjects and possibly collected from an array of sources, has become increasingly common in the fields of engineering and scientific research. Integrative learning using the tools developed in this project has allowed us to gain important insights in a variety of real-world applications in genetics, finance, population health, among others. 

Throughout the project, we have pursued a comprehensive investigation and generalization of the so-called reduced-rank methodology, one of the most critical ingredients in modern multivariate statistical techniques, in order to advance it for large-scale multivariate/multi-view learning. We have progressed on three aspects. First, we investigated the fundamental properties of reduced-rank estimation, including its complexity measure (degrees of freedom) and unbiased risk estimation, model selection and diagnostics, robustification and outlier detection, nested or multi-scale reduced-rank structure, adaptive nuclear-norm penalization for improving bias-variance tradeoff, and composite nuclear-norm penalization for dimension reduction with multi-view feature sets. Second, we investigated the integration of reduced-rank structure with other indispensable data attributes and modeling elements, such as sparsity, feature grouping, dynamic association, missing data, data heterogeneity, etc. For example, we have developed a series of sparse and low-rank methods for simultaneous dimension reduction and variable selection, such as sparse and orthogonal factor regression for association network learning, Bayesian sparse and low-rank models for inference making, generalized sparse and low-rank models with mixed-type responses, divide-and-conquer and stagewise learning approaches for scalable computation, among others. Third, we investigated the integration of disparate but interrelated learning objectives with multi-view data, such as simultaneous feature construction and predictive modeling. With this project, the potentials of the reduced-rank methodology have been better realized and understood for handling multivariate and multi-view data in joint learning, shared learning, multi-scale learning and robust learning. 

The project has involved training of several Ph.D. students. More than 20 papers have been published in leading statistical and machine learning journals, and several R packages have been developed and distributed on CRAN. 

Last Modified: 11/11/2020
Modified by: Kun Chen