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

arXiv: https://arxiv.org/abs/2606.17267 · HTML: https://mlsanity.com/paper/2606.17267/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 60 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
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- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Infinite Edge Partition Models for Overlapping Community Detection and Link Prediction](https://mlsanity.com/paper/1501.06218/) (2015)
- [Bayesian Tensor Regression](https://mlsanity.com/paper/1509.06490/) (2015)
- [Factor Models for High-Dimensional Tensor Time Series](https://mlsanity.com/paper/1905.07530/) (2019)
- [Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Counts](https://mlsanity.com/paper/1506.03493/) (2015)
- [Gamma Belief Networks](https://mlsanity.com/paper/1512.03081/) (2015)
- [Fast Network Community Detection with Profile-Pseudo Likelihood Methods](https://mlsanity.com/paper/2011.00647/) (2020)
- [Hierarchical Compound Poisson Factorization](https://mlsanity.com/paper/1604.03853/) (2016)
- [Tensor PCA for Factor Models](https://mlsanity.com/paper/2212.12981/) (2022)
- [Restricted Tweedie Stochastic Block Models](https://mlsanity.com/paper/2310.10952/) (2023)
- [Near-Universal Multiplicative Updates for Nonnegative Einsum Factorization](https://mlsanity.com/paper/2602.02759/) (2026)
- [Bayesian Dynamic Tensor Regression](https://mlsanity.com/paper/1709.09606/) (2017)
- [Doubly Non-Central Beta Matrix Factorization for Stable Dimensionality Reduction of Bounded Support Matrix Data](https://mlsanity.com/paper/2410.18425/) (2024)

## Abstract (arXiv)

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.