Locally weighted projection regression (LWPR) is a new algorithm for incremental nonlinear function approximation in high dimensional spaces with redundant and irrelevant input dimensions. At its core, it employs nonparametric regression with locally linear models. In order to stay computationally e#cient and numerically robust, each local model performs the regression analysis with a small number of univariate regressions in selected directions in input space in the spirit of partial least...