10. Mixed Integer Programming for Feature Selection in Scalar-on-Function Regression

Feature selection is a critical challenge in model selection, particularly for functional data, where appropriate statistical methodologies remain underdeveloped. This study investigates the application of Mixed Integer Programming (MIP) combined with information criteria for best feature subset selection in scalar-on-function regression (i.e., regression models where predictors are curves). Transforming the functional regression problem into a classic linear model framework with grouped variables allows the use of model selection criteria such as Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Generalized Cross Validation (GCV), in combination with MIP. In simulation studies, we compared our MIP method to alternative approaches and found that it consistently identifies truly active features.

Functional data analysis

Mixed Integer Programming

Model Selection 

Beginner

Knowledge

Women in Statistics and Data Science 2025