topological techniques in model selection

Abstract

This paper is concerned with enhancing the performance of Lasso for squarefree hierarchical polynomial models. We propose a compound crite- rion that combines validation error with a measure of model complexity, and the measure of model complexity is a sum of Betti numbers of the model, seen as a simplicial complex. The compound criteria helps model selection in polynomial regression models containing higher-order interactions. Sim- ulation results and a real data example show that the compound criteria produces sparser models with lower prediction errors than other statistical methods.