  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.
