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

2026-06-17 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning, Economic Analysis & Policy · Depth: Expert, extended

Summary

The Bayesian Poisson-Randomized Gamma Tensor Factorization (BPRGTF) model addresses sparse semi-continuous tensor data characterized by excess zeros, heavy right tails, and slice-specific dispersion. This hierarchical model applies a low-rank CP structure to a latent Poisson rate tensor, coupled with a conditional Gamma model for positive outcomes, allowing rate parameters to vary across slices. It effectively separates the occurrence and magnitude of positive observations while borrowing strength across all tensor dimensions. Posterior inference scales to large arrays via a hybrid variational–Monte Carlo algorithm. Applied to approximately 60 million international trade flows (151 countries, 96 products, 27 years), BPRGTF surfaces multiway dependence across exporters, importers, products, and years, which is difficult to recover using traditional methods.

Key takeaway

For research scientists analyzing sparse, semi-continuous multiway data, this Bayesian Poisson-randomized Gamma tensor factorization offers a robust approach. You can effectively model datasets with excess zeros and heterogeneous dispersion, such as international trade flows, to uncover complex, interpretable multiway dependence patterns. Consider applying this hybrid inference method to reveal structural insights in large-scale economic, biological, or epidemiological tensors, where traditional methods fall short in jointly modeling multiple dimensions.

Key insights

A Bayesian Poisson-randomized Gamma tensor factorization models sparse, semi-continuous multiway data with excess zeros and heterogeneous dispersion.

Principles

• Separate occurrence and magnitude for semi-continuous data.
• Allow dispersion to vary across tensor modes.
• Hybrid variational-Monte Carlo enables large-scale inference.

Method

Combines Poisson-randomized Gamma likelihood with low-rank CP structure, using a hybrid variational–Monte Carlo algorithm with binary activity indicators for scalable inference.

In practice

• Analyze international trade flows for multiway dependence.
• Apply to drug-response, species-abundance, or healthcare data.

Topics

• Bayesian Tensor Factorization
• Poisson-Gamma Models
• Semi-continuous Data
• International Trade Analysis
• Variational Inference
• CP Decomposition
• Sparse Data Modeling

Best for: AI Scientist, Research Scientist, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.