Near-optimal Nonlinear Regression Trees

Abstract We propose Near-optimal Nonlinear Regression Trees with hyperplane splits (NNRTs) that use a polynomial prediction function in the leaf nodes, which we solve by stochastic gradient methods. On synthetic data, we show experimentally that the algorithm converges to the global optimal. We compare NNRTs, ORT-LH, Multivariate Adaptive Regression Splines (MARS), Random Forests (RF) and XGBoost on 40 real-world datasets and show that overall NNRTs have a performance edge over all other methods.