Session 1: High-dimensional Tensor Data Analysis

Session title: High-dimensional Tensor Data Analysis
Organizer: Xin “Henry” Zhang (Florida State U)
Chair: Xin “Henry” Zhang (Florida State U)
Time: June 4th, 9:00-10:30am
Location: VEC 404/405

Speech 1: Multilayer Tensor Factorization with Applications to Recommender Systems
: Xuan Bi (Yale)
abstract: Recommender systems have been widely adopted by electronic commerce and entertainment industries for individualized prediction and recommendation, which benefit consumers and improve business intelligence. In this talk, we propose an innovative method, namely the recommendation engine of multilayers (REM), for tensor recommender systems. The proposed method utilizes the structure of a tensor response to integrate information from multiple modes, and creates an additional layer of nested latent factors to accommodate between-subjects dependency. One major advantage is that the proposed method is able to address the “cold-start” issue in the absence of information from new customers, new products or new contexts. Specifically, it provides more effective recommendations through sub-group information. To achieve scalable computation, we develop a new algorithm for the proposed method, which incorporates a maximum block improvement strategy into the cyclic blockwise-coordinate-descent algorithm. In theory, we investigate algorithmic properties for convergence from an arbitrary initial point and local convergence, along with the asymptotic consistency of estimated pa- rameters. Finally, the proposed method is applied in simulations and IRI marketing data with 116 million observations of product sales. Numerical studies demonstrate that the proposed method outperforms existing competitors in the literature.

Speech 2: Dynamic Tensor Clustering
Will Wei Sun (University of Miami)
abstract: Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap between statistical guarantee and computational efficiency for existing tensor clustering solutions. In this talk, I will introduce a new dynamic tensor clustering method, which takes into account both sparsity and fusion structures, and enjoys strong statistical guarantees as well as high computational efficiency. The efficacy of our approach will be illustrated via two real applications: brain dynamic functional connectivity analysis, and advertisement clustering for market segmentation. This is a joint work with Lexin Li.

Speech 3: Covariate-adjusted tensor classification in high-dimensions
Qing Mai (Florida State U)
abstract: In contemporary scientific research, it is of great interest to predict a categorical response based on a high-dimensional tensor and additional covariates. We introduce the CATCH model (in short for Covariate-Adjusted Tensor Classification in High-dimensions), that efficiently integrates the covariates and the tensor to predict the categorical outcome and jointly explains the relationships among the covariates, the tensor predictor, and the categorical response. To tackle the new computational and statistical challenges arising from the intimidating tensor dimensions, we propose a group penalized approach and an efficient algorithm. Theoretical results confirm that our method achieves variable selection consistency and optimal prediction, even when the tensor dimension is much larger than the sample size. The superior performance of our method over existing methods is demonstrated in extensive simulation studies, a colorimetric sensor array data, and two neuroimaging studies.