Contributions to the Lasso method and extensions

• Grant number: 20/16334-9
• Support Opportunities: Scholarships abroad - Research
• Start date: January 10, 2022
• End date: January 09, 2023
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Gustavo Henrique de Araujo Pereira
• Grantee: Gustavo Henrique de Araujo Pereira
• Host Investigator: Jianwen Cai
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: University of North Carolina at Chapel Hill (UNC), United States

Abstract

Lasso is a widely used method for parameter estimation in parametric regression models. Part of its success lies on the fact that it gives better predictive power than traditional methods such as least squares or maximum likelihood. In addition, Lasso still uses the easy-to-interpret components of parametric regression models. However, it is often the case that Lasso has worse predictive power than non-parametric regression models, which are usually hard to interpret. This project proposes modifications in Lasso or in one of the extensions of the method so that its predictive power gets closer to the best non-parametric models. Our methods will be especially useful in settings where one wants to use the estimated regression to get accurate predictions as well as to get explanations. (AU)