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Bayesian Boolean Matrix Factorisation
Tammo Rukat · Christopher Holmes · Michalis Titsias · Christopher Yau

Mon Aug 07 01:30 AM -- 05:00 AM (PDT) @ Gallery #80

Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two 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 Boolean matrix factorisation and derive a Metropolised Gibbs sampler that facilitates efficient parallel posterior inference. On real world and simulated data, our method outperforms all currently existing approaches for Boolean matrix factorisation and completion. This is the first method to provide full posterior inference for Boolean Matrix factorisation which is relevant in applications, e.g. for controlling false positive rates in collaborative filtering and, crucially, 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 thousand genes on commodity hardware.

Author Information

Tammo Rukat (University of Oxford)
Christopher Holmes (University of Oxford)
Michalis Titsias (Athens University of Economics and Business)
Christopher Yau (University of Birmingham)

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