Lasso for hierarchical polynomial models

Abstract The divisibility conditions implicit in a polynomial hierarchy suggest parameter constraints in regression. With this idea, we establish strong and weak hierarchies for both the lasso and relaxed lasso. Our proposal extends prior work on hierarchical lasso, which was mainly concerned with models of degree 2. The implementation of our methods uses existing quadratic programming techniques, and we apply them to both simulated data and examples from the literature. The empirical results compare favourably with existing techniques in terms of low validation error and model size.