Statistics Seminar

Abstract: Datasets in the social and biomedical sciences often consist of interactions among some set of units, such as events between countries in international relations or combinations of drugs in pharmacology. Such datasets are often represented as sparse tensors that store the observed count of all possible interactions. A natural framework for analyzing such data is tensor decomposition. In particular, non-negative Tucker decomposition unifies and generalizes a wide range of statistical network models and yields an interpretable “parts-based” representation that often surfaces scientifically meaningful latent structure. However, the practical application of Tucker-based models is hampered by combinatorial explosion in their parameter space which grows exponentially in the number of modes of the input tensor. This problem is especially severe in multiway networks, where there are multiple types of interactions, and in hypergraphs, where groups of nodes interact. In this talk, I will present new scalable approaches to non-negative Tucker models which retain their expressive power while avoiding their usual exponential blowup by constraining the latent "core" tensors to be either sparse or low-rank. I illustrate these approaches first on multilayer networks of country-to-country events and then on hypergraphs of bill cosponsorship and drug-drug interactions, showing how such models can tractably capture a broad spectrum of "mesoscale" structure.