Clustering and feature screening in Functional regression model by Variational Inference.

• Grant number: 24/22101-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2025
• End date: April 30, 2027
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Aluísio de Souza Pinheiro
• Grantee: Giovanni Pastori Piccirilli
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/02538-0 - Time series, wavelets, high dimensional data and applications, AP.TEM
• Associated scholarship(s): 25/27107-7 - Bayesian wavelet change detection using multiple data sets in urban areas, BE.EP.PD 25/27106-0 - Slow sliding area detection by Bayesian wavelet methods, BE.EP.PD

Abstract

This project proposes new statistical approaches to the problem of variable selection in functional regression models using the Bayesian paradigm. Although frequentist methodologies are well understood, using Bayesian inference in functional data has still not been explored. Variational inference techniques, widely applied in Statistical Machine Learning, demonstrate great efficiency, but their application in functional data presents challenges, especially in high-dimensional models. The goal is to develop accurate and computationally efficient methods, including integrating Bayesian Conditional Transformations and expanding their applicability in highly complex scenarios. (AU)