A Joint Bayesian Boolean Matrix Factorization with Application to Chromosomal Copy Number Alterations in Multiple Myeloma

2026-08-03

AI Summary

This work addresses the challenge of effectively modeling both shared and condition-specific latent structures across multiple related binary datasets, which existing Boolean matrix factorization methods struggle to capture. To this end, the authors propose a Joint Bayesian Boolean Matrix Factorization (JBBMF) model that simultaneously decomposes two associated binary matrices by leveraging a shared latent pattern matrix and condition-specific priors. The approach coherently characterizes the stability and variation of latent factors across conditions while preserving interpretability and enabling uncertainty quantification. Built upon Boolean factorization, Bernoulli observation likelihoods, conjugate priors, and an efficient Gibbs sampling scheme for posterior inference, JBBMF demonstrates superior performance over independent decomposition baselines. Experiments reveal its ability to successfully identify chromosomal copy number aberration patterns shared between diagnostic and relapse stages in multiple myeloma, along with reliable uncertainty estimates.

Abstract

Boolean matrix factorization provides an interpretable framework for discovering latent binary patterns in high-dimensional data, yet existing methods typically analyze a single binary matrix or factorize multiple matrices independently, failing to exploit shared latent structure across related datasets. We propose Joint Bayesian Boolean Matrix Factorization (JBBMF), a model that simultaneously factorizes two related binary matrices through a shared latent Boolean pattern matrix and dataset-specific loading matrices. To capture dependence between paired datasets, we introduce a conditional prior linking the loading matrices, allowing latent factors to persist or change across conditions while preserving a common interpretable representation. The model combines Boolean matrix factorization with a Bernoulli observation model and conjugate priors, yielding closed-form full conditional distributions and an efficient Gibbs sampler for posterior inference,uncertainty quantification for latent factors, reconstructed matrices, and noise parameters. Simulation studies demonstrate that jointly modeling related binary datasets substantially improves recovery of shared latent factors compared with independently applying standard Boolean matrix factorization to each dataset, while maintaining high reconstruction accuracy. We apply JBBMF to paired chromosomal copy number alteration profiles from multiple myeloma patients collected at diagnosis and relapse. The analysis identifies recurrent chromosomal alteration signatures shared between disease stages and quantifies the uncertainty of these findings. \texttt{JBBMF} offers a flexible and interpretable Bayesian model for the joint analysis of related binary datasets in genomics and other application domains.

Problem

• Boolean matrix factorization
• joint analysis
• shared latent structure
• binary data
• multiple datasets

Innovation

• Joint Bayesian Boolean Matrix Factorization
• Boolean matrix factorization
• shared latent structure
• conditional prior
• Gibbs sampling