# Compressive Bayesian non-negative matrix factorization for mutational signatures analysis

arXiv: https://arxiv.org/abs/2404.10974 · HTML: https://mlsanity.com/paper/2404.10974/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2024.

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

- [Inference on covariance structure in high-dimensional multi-view data](https://mlsanity.com/paper/2509.02772/) (2025)
- [Overfitted high-dimensional matrix factorizations via adaptive spectral shrinkage](https://mlsanity.com/paper/2606.19540/) (2026)
- [A New Family of Poisson Non-negative Matrix Factorization Methods Using the Shifted Log Link](https://mlsanity.com/paper/2601.05845/) (2026)
- [VAE-MS: An Asymmetric Variational Autoencoder for Mutational Signature Extraction](https://mlsanity.com/paper/2602.22239/) (2026)
- [Large-scale empirical tuning and comparison of default optimizers for variational inference](https://mlsanity.com/paper/2606.07841/) (2026)

## Abstract (arXiv)

Non-negative matrix factorization (NMF) is a popular tool for dimensionality reduction, especially for count matrices. However, inferring an appropriate number of factors is challenging. Existing approaches based on information criteria or nonparametric sparsity-inducing priors tend to be computationally burdensome or highly sensitive to prior choices. Moreover, theoretical properties of the posterior distribution of Poisson NMF parameters endowed with shrinkage priors remain under-explored. This paper introduces a novel Bayesian NMF method that automatically infers the number of factors while also incorporating information on the latent factors from previous studies. This is achieved using compressive hyperpriors, which are hierarchical priors that make the sample-specific weights of unneeded factors concentrate near zero in the posterior. We provide novel distribution theory for posterior inference to elucidate this shrinkage mechanism, both in finite samples and asymptotically. We apply our method to mutational signatures analysis in cancer genomics, in simulations and on real data from breast cancer. Compared to state-of-the-art alternatives, our method is more robust to mild overdispersion and improves detection and estimation of signatures aligned with prior information.