# Bayesian Nonparametric Boolean Factor Models

## TL;DR

This paper introduces a Bayesian nonparametric Boolean factor model using an Indian Buffet Process prior, enabling flexible latent dimension inference and scalable, efficient posterior inference for large-scale Boolean matrix and tensor factorization.

## Contribution

It extends existing Boolean factor models by removing the fixed number of latent factors constraint through an IBP prior, simplifying posterior inference and enhancing scalability.

## Key findings

- Achieved accurate Boolean matrix factorization on large datasets.
- Demonstrated efficient inference with billions of observations.
- Applied model successfully to a real-world dataset with 6 million entries.

## Abstract

We build upon probabilistic models for Boolean Matrix and Boolean Tensor factorisation that have recently been shown to solve these problems with unprecedented accuracy and to enable posterior inference to scale to Billions of observation. Here, we lift the restriction of a pre-specified number of latent dimensions by introducing an Indian Buffet Process prior over factor matrices. Not only does the full factor-conditional take a computationally convenient form due to the logical dependencies in the model, but also the posterior over the number of non-zero latent dimensions is remarkably simple. It amounts to counting the number false and true negative predictions, whereas positive predictions can be ignored. This constitutes a very transparent example of sampling-based posterior inference with an IBP prior and, importantly, lets us maintain extremely efficient inference. We discuss applications to simulated data, as well as to a real world data matrix with 6 Million entries.