DMS Statistics and Data Science Seminar

Speaker: Tobia Boschi (IBM Research, Dublin)

Title: FAStEN: An efficient adaptive method for feature selection and estimation in high-dimensional functional regressions

Abstract: Functional regression analysis is an established tool active for many contemporary scientific applications. Regression problems involving large and complex data sets are ubiquitous, and feature selection is crucial for avoiding overfitting and achieving accurate predictions. We propose a new, flexible and ultra-efficient approach to perform feature selection in a sparse high dimensional function-on-function regression problem. We show how to extend it to the scalar-on-function and concurrent regression frameworks. Our method combines functional data, optimization, and machine learning techniques to perform feature selection and parameter estimation simultaneously. We exploit the properties of Functional Principal Components and the sparsity inherent to the Dual Augmented Lagrangian problem to significantly reduce the computational cost, and we introduce an adaptive scheme to improve selection accuracy. Through an extensive simulation study, we benchmark our approach to the best existing competitors and demonstrate a massive gain in terms of CPU time and selection performance without sacrificing the quality of the coefficients' estimation. Finally, we present an application to brain fMRI data from the AOMIC PIOP1 study.