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Title: Logical factorisation machines : probabilistic Boolean factor models for binary data
Author: Rukat, Tammo
ISNI:       0000 0004 7966 2508
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2018
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Logical Factorisation Machines (LFMs) are a class of latent feature models, that aim to decompose binary matrices, tensors or higher-arity relations into an approximate logical product of low rank, binary matrices. These products are defined through the use of logical operators instead of arithmetic operations. The resulting factor matrices contain interpretable patterns that lend themselves to the discovery of hidden causal structure. We frame LFMs as probabilistic generative models and derive sampling based posterior inference. Despite full uncertainty quantification, the inference procedure scales to Billions of data points which is possible through exploitation of the logical structure in the factor conditionals. OrMachines are a particularly interesting subset of LFMs, where a single latent cause is sufficient to explain an outcome. They represent a probabilistic approach to the well-studied problems of Boolean Matrix Factorisation and Boolean Tensor Factorisation. The proposed model and inference procedure yield decompositions of higher accuracy than the existing techniques throughout a wide range of conditions. Real-world examples include single-cell genomics, cancer genomics, relational and spatio-temporal data. We propose several extensions, including hierarchies of OrMachines for data integration and a Bayesian nonparametric approach to infer the latent dimensionality. LFMs with less established logics, their relationships and interpretation are considered. While the latent structure in many of these models is inherently difficult to recover, we demonstrate that certain LFMs can provide complementary representations and reveal new findings. A fast and flexible implementation is introduced and publicly available on GitHub.
Supervisor: Holmes, Chris ; Yau, Chris Sponsor: EPSRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Machine learning--Statistical methods