Classification based two-sample tests for functional data

Project ID: 2228cd1428 (You will need this ID for your application)

UCL Lead department: Statistical Science

Project Summary:

The availability of large amounts of real-time data has prompted the need for the development of data-intensive methods for functional data analysis. In particular, there is a growing importance in studying two-sample tests for functional data. Although classification models and two-sample tests have been studied independently in this context, the differentiating power of classification models has yet to be explored to enhance the design of two-sample tests. Furthermore, the impact of variable selection on both classification methods and two-sample tests remains to be investigated. Given the abundance of functional data sets, these developments have wide-ranging applications, spanning from finance and health data science to retail analytics

The main objective of this project is to investigate the relationship between classification models, particularly their accuracy, and the k-sample test, and develop a novel nonparametric k-sample test, in the functional data context. The accuracy of classifiers has been utilised to design novel two-sample tests within the multivariate (high-dimensional) setting. This project aims to extend this analysis from both theoretical and methodological perspectives within the functional data context, introducing certain constraints to the existing framework.

The student will be jointly supervised at UCL by Prof Ioanna Manolopoulou, whose research focuses on developing statistical models to produce interpretable inferences in practical applications. She has extensive experience from supervision and co-supervision of PhD students. Dr Purvasha Chakravarti, Lecturer (Assistant Professor) in Statistical Science, whose research focuses on developing scalable and interpretable statistical inference methods for high-dimensional data. Dr Nicolás Hernández, Senior Research Fellow, working on statistical inference methods for high-dimensional and functional data.

Applicants should have a strong background (e.g. Master’s degree) in statistics, machine learning or a closely related field, and research interests in one or more of: functional data analysis, statistical inference, high-dimensional statistics. Strong programming skills (e.g. R, Python) are also desirable.