# Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Counts

arXiv: https://arxiv.org/abs/1506.03493 · HTML: https://mlsanity.com/paper/1506.03493/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2015.

## Built on by (most cited first, 19 of 19)

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- [Poisson-Gamma Dynamical Systems with Time-varying Transition Dynamics](https://mlsanity.com/paper/2609.00896/) (2026)
- [Dynamic Latent Space Modeling of Inhomogeneous Poisson Network Processes with Applications to International Relations](https://mlsanity.com/paper/2609.08813/) (2026)

## Abstract (arXiv)

We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country i took action a toward country j at time t"---known as dyadic events---in order to form and test theories of international relations. We represent these event data as a tensor of counts and develop Bayesian Poisson tensor factorization to infer a low-dimensional, interpretable representation of their salient patterns. We demonstrate that our model's predictive performance is better than that of standard non-negative tensor factorization methods. We also provide a comparison of our variational updates to their maximum likelihood counterparts. In doing so, we identify a better way to form point estimates of the latent factors than that typically used in Bayesian Poisson matrix factorization. Finally, we showcase our model as an exploratory analysis tool for political scientists. We show that the inferred latent factor matrices capture interpretable multilateral relations that both conform to and inform our knowledge of international affairs.