Probabilistic Tensor Modelling and Applications in the Life Sciences

Research output: Book/ReportPh.D. thesis

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This thesis concerns Bayesian matrix and tensor decomposition and the development of a publicly available probabilistic tensor toolbox. Decomposition methods are widely used and highly useful for determining latent patterns in data. Applications include nding underlying neural signals in electroencephalography, common genetic proles from gene expression data, and determining pure chemical spectras from samples with mixed spectras.
This toolbox provides a probabilistic framework for common tensor decomposition models, such as the Candecomp/PARAFAC (CP), Tucker and Tensor Train Decomposition. The main focus is probabilistic CP with and without constraints on the latent factors. Estimation from fully and partially observed data is considered, as is prediction on held-out slices or blocks of a tensor. Finally, it is possible to model residual noise following homoscedastic or mode specic heteroscedastic noise variance assumptions.
For learning the distribution of the latent parameters, fully Bayesian methods are used, specically variational Bayesian inference and Gibbs sampling. Bayesian methods facilitates uncertainty quantication, more realistic noise modelling, automatic model order selection, model comparison, and a principled way of incorporating a priori information.
This thesis serves as an introduction to Bayesian tensor decomposition and provides an overview of current state-of-art. The developed probabilistic tensor toolbox is useful for researchers looking to apply Bayesian tensor methods and as a reference implementation for comparison with existing and new tensor methods.
Original languageEnglish
PublisherTechnical University of Denmark
Number of pages197
Publication statusPublished - 2020


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