# Bayesian factorizations of big sparse tensors

arXiv: https://arxiv.org/abs/1306.1598 · HTML: https://mlsanity.com/paper/1306.1598/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2013.

## Built on by (most cited first, 5 of 5)

- [Multifile Partitioning for Record Linkage and Duplicate Detection](https://mlsanity.com/paper/2110.03839/) (2021)
- [The ALℓ0CORE Tensor Decomposition for Sparse Count Data](https://mlsanity.com/paper/2403.06153/) (2024)
- [Joint Bayesian Parameter and Model Order Estimation for Low-Rank Probability Mass Tensors](https://mlsanity.com/paper/2410.06329/) (2024)
- [Bayesian Federated Cause-of-Death Classification and Quantification Under Distribution Shift](https://mlsanity.com/paper/2505.02257/) (2025)
- [Bayesian Tensor Decomposition with Diffusion Model Prior](https://mlsanity.com/paper/2606.03212/) (2026)

## Abstract (arXiv)

It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics. The most common low rank tensor factorization relies on parallel factor analysis (PARAFAC), which expresses a rank k tensor as a sum of rank one tensors. When observations are only available for a tiny subset of the cells of a big tensor, the low rank assumption is not sufficient and PARAFAC has poor performance. We induce an additional layer of dimension reduction by allowing the effective rank to vary across dimensions of the table. For concreteness, we focus on a contingency table application. Taking a Bayesian approach, we place priors on terms in the factorization and develop an efficient Gibbs sampler for posterior computation. Theory is provided showing posterior concentration rates in high-dimensional settings, and the methods are shown to have excellent performance in simulations and several real data applications.