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Probabilistic Boolean Tensor Decomposition
Tammo Rukat · Christopher Holmes · Christopher Yau

Thu Jul 12 02:00 AM -- 02:20 AM (PDT) @ K11

Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules 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 estimates consistently outperform existing non-probabilistic approaches. We show that our performance gains can partially be explained by convergence to solutions that occupy relatively large regions of the parameter space, as well as by implicit model averaging. Moreover, the Bayesian treatment facilitates model selection with much greater accuracy than the previously suggested minimum description length based approach. We investigate three real-world data sets. First, temporal interaction networks 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

Author Information

Tammo Rukat (University of Oxford)
Christopher Holmes (University of Oxford)
Christopher Yau (University of Birmingham)

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