Title: MARS via LASSO
Abstract: MARS is a popular method for nonparametric regression proposed by Friedman in 1991. MARS fits simple nonlinear and non-additive functions to regression data. We propose and study a natural LASSO variant of the MARS method. Our method is based on least squares estimation over a convex class of functions obtained by considering infinite-dimensional linear combinations of functions in the MARS basis and putting a variation based complexity constraint. Our method is naturally connected to nonparametric function estimation methods under smoothness constraints. Under natural design assumptions, we prove that our estimator achieves a rate of convergence that depends only logarithmically on dimension and thus avoids the usual curse of dimensionality to some extent. This is joint work with Dohyeong Ki (UC Berkeley) and Billy Fang (Google).