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.
Keywords
regression, Lasso, topology, Betti numbers, model selection