# Scalable Bayesian Non-Negative Tensor Factorization for Massive Count Data

arXiv: https://arxiv.org/abs/1508.04211 · HTML: https://mlsanity.com/paper/1508.04211/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2015.

## Built on by (most cited first, 2 of 2)

- [Nonparametric Embeddings of Sparse High-Order Interaction Events](https://mlsanity.com/paper/2207.03639/) (2022)
- [Robust Bayesian Tensor Factorization with Zero-Inflated Poisson Model and Consensus Aggregation](https://mlsanity.com/paper/2308.08060/) (2023)

## Abstract (arXiv)

We present a Bayesian non-negative tensor factorization model for count-valued tensor data, and develop scalable inference algorithms (both batch and online) for dealing with massive tensors. Our generative model can handle overdispersed counts as well as infer the rank of the decomposition. Moreover, leveraging a reparameterization of the Poisson distribution as a multinomial facilitates conjugacy in the model and enables simple and efficient Gibbs sampling and variational Bayes (VB) inference updates, with a computational cost that only depends on the number of nonzeros in the tensor. The model also provides a nice interpretability for the factors; in our model, each factor corresponds to a "topic". We develop a set of online inference algorithms that allow further scaling up the model to massive tensors, for which batch inference methods may be infeasible. We apply our framework on diverse real-world applications, such as multiway topic modeling on a scientific publications database, analyzing a political science data set, and analyzing a massive household transactions data set.