Statistics & Data Science Colloquium

Title Tensor modeling in categorical data analysis and conditional association studies

Abstract  In this talk, we offer new tensor perspectives for two classical multivariate analysis problems. First, we consider the regression of multiple categorical response variables on a high-dimensional predictor. A $M$-th order probability tensor can efficiently represent the joint probability mass function of the $M$ categorical responses. We propose a new latent variable model based on the connection between the conditional independence of the responses and the rank of their conditional probability tensor. We develop a regularized expectation-maximization algorithm to fit this model and apply our method to modeling the functional classes of genes. Second, we consider the three-way associations of how two sets of variables associate and interact, given another set of variables. We establish a population dimension reduction model, transform the problem to sparse Tucker tensor decomposition, and develop a higher-order singular value decomposition estimation algorithm. We demonstrate the efficacy of the method through a multimodal neuroimaging application for Alzheimer's disease research.