Jesper Løve Hinrich: We live in a digital society in which information is gathered in more and more detail from our interactions on social media, smartphones to medical records and biomedical sensors. This information can be used quantify our physical and mental state. For example using brain imaging and genome sequencing to understand neurological disease or the influence of genetic variations.
Information collection and analysis is widespread in all areas of science, and the increased use of multiple high speed and/or high resolution sensors lets information be gathered in much finer detail than ever before. However, the resulting multi-modal datasets are difficult to analyze as most method are currently based on two-mode (matrix) modeling, which is problematic when faced with higher order tensor data, i.e. greater than two modes.
Tensor methods account for this multi-modal structure and have been successful in a wide range of fields. Current practices are based on point estimates (i.e. maximum likelihood), which can be unstable to small changes and does not provide parameter uncertainties for the estimated model. Therefore, we investigate fully Bayesian modeling, which is a type of probabilistic modeling that allows for handling parameter uncertainty in a natural way and facilitates joint inference of model order and parameters.
Probabilistic modeling of tensor decomposition methods is in its infancy and currently restricted to the basic Tucker and Canonical Polydiac decomposition along with a few simple constraints. The aim of this PhD project is to develop a high-performance open source toolbox. Providing a collection of basic and advanced probabilistic tensor decomposition methods, as well as tools for model selection and validation. The developed methods will be use to address current challenges in the Life Sciences, specifically within neuroimaging, genetics and chemometrics.
PhD project title:
A Probabilistic Framework for Tensor Methods with Applications in the Life Sciences
Effective start/end date 01/01/2017 → 31/12/2019
DTU supervisor: Morten Mørup, section for Cognitive Systems at DTU Compute.