Nonparametric Functional Approximation with Delaunay Triangulation Learner

We propose a differentiable nonparametric algorithm, the Delaunay triangulation learner (DTL), to solve the functional approximation problem on the basis of a p-dimensional feature space. By conducting the Delaunay triangulation algorithm on the data points, the DTL partitions the feature space into a series of p-dimensional simplices in a geometrically optimal way, and fits a linear model within each simplex. We study its theoretical properties by exploring the geometric properties of the Delaunay triangulation, and compare its performance with other statistical learners in numerical studies.