Abstract

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

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