Probabilistic boolean tensor decomposition

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Authors

Colleges, School and Institutes

External organisations

  • Department of Statistics, Oxford University, Oxford, UK

Abstract

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

Details

Original languageEnglish
Title of host publicationVolume 80
Subtitle of host publicationInternational Conference on Machine Learning, 10-15 July 2018, Stockholmsmässan, Stockholm Sweden
EditorsJennifer Dy, Andreas Krause
Publication statusPublished - 10 Jul 2018
EventThe 35th International Conference on Machine Learning (ICML 2018) - Stockholmsmässan, Stockholm , Sweden
Duration: 10 Jul 201815 Jul 2018

Publication series

NameProceedings of Machine Learning Research
PublisherProceedings of Machine Learning Research
Volume80
ISSN (Electronic)1938-7228

Conference

ConferenceThe 35th International Conference on Machine Learning (ICML 2018)
Abbreviated titleICML 2018
CountrySweden
CityStockholm
Period10/07/1815/07/18