Persistent Homology in Statistical Model Building

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Variable selection in statistical modelling is concerned with the question of choosing the most relevant explanatory variables from a potentially large set of candidates.The goal is to achieve a good fit between a model and data without including too many variables. The main objective of this project is to adapt methods from the topological theory of persistent homology in order to develop new variable selection techniques. The proposal combines model description from the point of view of computational algebra with statistical methods such as the Lasso technique and Bayesian model selection.Partners from network modeling, climate modeling and from robust engineering and design will provide data which will be used in case studies to assess the performance of the new methods. Also, the project will scope the use of software for combining topological and statistical algorithms, which will enable researchers to combine the different approaches without having to do extensive programming. Methodological results from this project have the potential to be applied to the analysis of large data sets in areas where the detection of interactions between explanatory variables is crucial.