Tensor Models for Large, Complex and High-Dimensional Data

• Activity Number: 392 - Big Tensor Data Analysis
• Type: Invited
• Date/Time: Wednesday, August 5, 2020 : 1:00 PM to 2:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Shuheng Zhou*
• Companies: University of California, Riverside
• Keywords: Matrix normals; Precision matrix; Complex data analysis; genomic studies; spatio-temporal modeling; conditional independence relation

Abstract

Building models and methods for complex data is an important task for many scientific and application areas. I will discuss several interrelated yet distinct models and methods on graph and mean recovery problems with applications in spatio-temporal modeling and genomics. For genomics studies, many datasets exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing high-dimensional data with unknown mean and dependence structures. I will present a practical method utilizing generalized least squares and penalized (inverse) covariance estimation to address this challenge. I will then introduce a multiway tensor generalization of the bigraphical lasso, an estimator for precision matrices of matrix-normals based on the Cartesian product of graphs. We call this tensor graphical lasso generalization the TeraLasso estimator. Statistical consistency and rates of convergence are established for both bigraphical and TeraLasso estimators for precision estimation. Data examples from a meteorological study will be presented to show that we can extract meaningful conditional dependency structures from large and complex datasets.