Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: Boolean matrix factorisation (BooMF) infers interpretable decompositions of a binary data matrix into a pair of low-rank, binary matrices: One containing meaningful patterns, the other quantifying how the observations can be expressed as a combination of these patterns. We introduce the OrMachine, a probabilistic generative model for BooMF and derive a Metropolised Gibbs sampler that facilitates very efficient parallel posterior inference. Our method outperforms all currently existing approaches for Boolean Matrix factorization and completion, as we show on simulated and real world data. This is the first method to provide full posterior inference for BooMF which is relevant in applications, e.g. for controlling false positive rates in collaborative filtering, and crucially it improves the interpretability of the inferred patterns. The proposed algorithm scales to large datasets as we demonstrate by analysing single cell gene expression data in 1.3 million mouse brain cells across 11,000 genes on commodity hardware.

Bayesian Boolean Matrix Factorisation