Statistically robust topological data analysis for biomedical applications

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Techniques from topological data analysis (TDA) have the ability to detect and quantify global properties of data, such as n-dimensional holes, representing a particular type of dependence of variables. The aim of this project is to investigate and enhance existing approaches from TDA, such as persistent homology, with statistical methods to make these robust to noise and small perturbations, and apply these techniques to clinically relevant data from the UK Biobank to examine a variety of biomedical questions, such as disease subtyping based on relevant molecular features.