Colloquium: "Tensor modeling in categorical data analysis and association studies"

Abstract: We present 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. A simple, intuitive, and interpretable latent variable model is proposed 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. Next, we study the three-way associations of how two sets of variables associate and interact, given another set of variables. This is motivated by a central question in the multimodal integrative data analysis -- how two data modalities associate and interact with each other given another modality or demographic covariates. 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. The new method is applied to a multimodal neuroimaging application for Alzheimer's disease research.

Host: Jose Figueroa-Lopez