• feature selection
• functional data analysis
• optimization

Functional regression analysis is establishing itself as an active and growing research topic. 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.
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 the 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 estimates. Finally, we present an application from the AOMIC PIOP1 study.