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.

介绍了一种概率生成模型 ——OrMachine，用于布尔矩阵分解和推导出马尔科夫链蒙特卡罗 (Metropolised Gibbs) 采样器，实现了高效的并行后验推断，并在真实世界和模拟数据上优于目前所有现有的布尔矩阵分解和完整方法，首次为布尔矩阵分解提供了完整的后验推断，在协同过滤中用于控制假阳性率，并关键地提高了推断模式的可解释性。提出的算法在通用硬件上扩展到大型数据集，如在 1.3 百万只老鼠脑细胞上分析 11 千个基因的单细胞基因表达。