TensOrMachine: Probabilistic Boolean Tensor Decomposition

TL;DR

This paper introduces TensOrMachine, a probabilistic Boolean tensor decomposition method that improves accuracy, scalability, and handling of missing data for binary multi-way data analysis, demonstrated on real-world datasets including gene expression in cancer.

Contribution

It presents the first probabilistic framework for Boolean tensor decomposition, enabling scalable inference, better accuracy, and effective missing data treatment.

Findings

Maximum a posteriori decompositions outperform existing techniques.

Scalable to tensors with over 10 billion data points.

Effective in uncovering latent patterns in real-world datasets.

Abstract

Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate scalable sampling-based posterior inference by exploitation of the combinatorial structure of the factor conditionals. Maximum a posteriori decompositions feature higher accuracies than existing techniques throughout a wide range of simulated conditions. Moreover, the probabilistic approach facilitates the treatment of missing data and enables model selection with much greater accuracy. We investigate three real-world data-sets. First, temporal interaction networks in a hospital ward and behavioural data of university students demonstrate the inference of instructive latent patterns. Next, we decompose a tensor with more than 10 billion data points, indicating relations of gene expression in cancer patients. Not only does this demonstrate scalability, it also provides an entirely novel perspective on relational properties of continuous data and, in the present example, on the molecular heterogeneity of cancer. Our implementation is available on GitHub: https://github.com/TammoR/LogicalFactorisationMachines.