Online Program Home
  My Program

All Times EDT

Abstract Details

Activity Number: 354 - Multivariate Analysis and Graphical Models
Type: Contributed
Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #313885
Title: Tensor Mixture Model in High Dimensions
Author(s): Biao Cai* and Emma Jingfei Zhang and Wei Sun
Companies: University of Miami and University of Miami and Purdue University
Keywords: Clustering; Heterogeneity; Tensor decomposition; Non-asymptotic error rate; Non-convex optimization

We consider the problem of modeling heterogeneous tensor-valued data by jointly clustering and estimating heterogeneous tensor graphical models. We assume the data follow a mixture tensor normal distribution, whose mixture mean and covariances are unknown. Our formulation greatly relaxes the assumptions in existing approaches, which usually require that the cluster structure is given and/or the covariances are known in advance. To tackle this challenging high-dimensional problem, we effectively exploit the inherit structures of the tensor-valued data. Specifically, we assume the mixture mean is low-rank and the mixture covariance has a Kronecker structure. We formulate the parameter estimation as a conditional EM (CEM) estimation problem, and develop an efficient alternating minimization CEM algorithm. In theory, we establish the non-asymptotic error bound for the actual estimator from our algorithm. The theoretical analysis is highly nontrivial due to the non-convex nature of both the CEM estimation and tensor decomposition. The derived error bound reveals an interesting interplay between computational efficiency and the statistical rate of convergence.

Authors who are presenting talks have a * after their name.

Back to the full JSM 2020 program