arXiv 15 Jun 2026 · Statistics — Methodology
arXiv:2606.17267 · PDF · DOI · OpenAlex · Extracted main text
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.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Schein, Aaron and Paisley, John and Blei, David M and Wallach, Hanna (2015) Bayesian Poisson tensor factorization for inferring multilateral relations from sparse dyadic event counts self | 1.000 | 5 | 5 | 100% |
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| 7 | Yuan, Lin and Kalbfleisch, John D (2000) On the Bessel distribution and related problems | 0.644 | 2 | 2 | 100% |
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| 9 | Gillis, Nicolas (2020) Nonnegative Matrix Factorization | 0.585 | 3 | 1 | 100% |
| 10 | Trade and Industry Department (2026) Hong Kong–Mainland Trade Relations (Overview/Factsheet) | 0.511 | 3 | 2 | 33% |
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