# A particle-based variational approach to Bayesian Non-negative Matrix Factorization

arXiv: https://arxiv.org/abs/1803.06321 · HTML: https://mlsanity.com/paper/1803.06321/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [A Simple and Scalable Tensor Completion Algorithm via Latent Invariant Constraint for Recommendation System](https://mlsanity.com/paper/2206.13355/) (2022)

## Abstract (arXiv)

Bayesian Non-negative Matrix Factorization (NMF) is a promising approach for understanding uncertainty and structure in matrix data. However, a large volume of applied work optimizes traditional non-Bayesian NMF objectives that fail to provide a principled understanding of the non-identifiability inherent in NMF-- an issue ideally addressed by a Bayesian approach. Despite their suitability, current Bayesian NMF approaches have failed to gain popularity in an applied setting; they sacrifice flexibility in modeling for tractable computation, tend to get stuck in local modes, and require many thousands of samples for meaningful uncertainty estimates. We address these issues through a particle-based variational approach to Bayesian NMF that only requires the joint likelihood to be differentiable for tractability, uses a novel initialization technique to identify multiple modes in the posterior, and allows domain experts to inspect a `small' set of factorizations that faithfully represent the posterior. We introduce and employ a class of likelihood and prior distributions for NMF that formulate a Bayesian model using popular non-Bayesian NMF objectives. On several real datasets, we obtain better particle approximations to the Bayesian NMF posterior in less time than baselines and demonstrate the significant role that multimodality plays in NMF-related tasks.