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

2026-06-15

AI Summary

This study addresses the modeling of sparse semi-continuous tensor data—such as international trade flows—characterized by high-dimensional sparsity, heavy-tailed positive values, and slice-specific discreteness. The authors propose a Bayesian hierarchical CP tensor decomposition model that jointly captures event occurrence (via Poisson rates) and magnitude (via conditional Gamma distributions) within a unified low-rank framework, thereby simultaneously accounting for zero inflation, heavy-tailed positive entries, and slice-level discrete parameters. By sharing a low-rank representation across exporter, importer, product, and time dimensions, the model transcends conventional gravity models and pairwise network analyses. A hybrid inference algorithm combining coordinate-ascent variational inference with a partially collapsed augmented sampler enables efficient learning from approximately 60 million trade records, effectively uncovering complex high-order interaction structures such as product–time dependencies.

Abstract

We study sparse semi-continuous tensor data with excess zeros, heavy right tails, and slice-specific dispersion. Such features arise naturally in monetary-valued multi-way data, such as international trade, where most exporter--importer--product--year cells are zero while positive values are continuous and highly variable. To model these data, we propose a Bayesian hierarchical tensor factorization model that places a low-rank CP structure on a latent Poisson rate tensor and couples it with a conditional Gamma model for positive outcomes, with rate parameters that can vary across slices within a mode. The model therefore separates the occurrence and magnitude of positive observations while borrowing strength across all tensor dimensions through a shared low-rank latent structure. To scale posterior inference to large arrays, we develop a hybrid variational--Monte Carlo algorithm that combines efficient coordinate ascent updates with a partially collapsed augmented-data sampler. Applied to approximately 60 million trade flows, the method surfaces multiway dependence across exporters, importers, products, and years that is difficult to recover from gravity-type or pairwise network analyses, which do not jointly model the product and temporal dimensions.

Problem

• sparse semi-continuous tensor
• excess zeros
• heavy right tails
• slice-specific dispersion
• international trade flows

Innovation

• Bayesian tensor factorization
• Poisson-Gamma mixture
• low-rank CP decomposition
• semi-continuous data
• hybrid variational-Monte Carlo inference