Title: Bayesian Poisson-Randomized Gamma Tensor Factorization with Application to International Trade Flows

Affiliation: University of Chicago

Abstract: 

We develop probabilistic machine learning methods for tensor data whose entries are nonnegative, semi-continuous, and exhibit excess zeros, heavy right tails, and slice-varying dispersion. Such a structure arises in monetary-valued multiway arrays, such as international trade, where most cells of the exporter × importer × product × year tensor are zero while positive entries span several orders of magnitude. We propose a Bayesian hierarchical model that combines a low-rank nonnegative CP decomposition with a compound Poisson--Gamma likelihood, and develop a hybrid variational--Monte Carlo algorithm for posterior inference, including an asymptotic approximation to a Bessel-family conditional that enables scalable computation for tensors with tens of millions of entries. Applied to international trade data, the model recovers interpretable multiway dependence across exporters, importers, products, and time that is inaccessible to methods operating on fewer tensor margins.