Abstract: Multidimensional arrays, or tensors, are becoming increasingly prevalent in a wide range of scientific applications. In this talk, I will present two case studies from neuroscience, where tensor decomposition proves particularly useful. The first study is a cross-area neuronal spike trains analysis, which we formulate as the problem of regressing a multivariate point process on another multivariate point process. We model the predictor effects through the conditional intensities using a set of basis transferring functions in a convolutional fashion. We then organize the corresponding transferring coefficients in the form of a three-way tensor, and impose the low-rank, sparsity, and subgroup structures on this coefficient tensor. The second study is a multimodal neuroimaging analysis for Alzheimer’s disease, which we formulate as the problem of modeling the correlations of two sets of variables conditioning on the third set of variables. We propose a generalized liquid association analysis method to study such three-way associations. We establish a population dimension reduction model, and transform the problem to sparse decomposition of a three-way tensor.