Nonparametric Functional Approximation with Delaunay Triangulation
This work addresses functional approximation for statistical learning, but it appears incremental as it builds on existing triangulation methods.
The authors tackled the functional approximation problem in a p-dimensional feature space by proposing the Delaunay triangulation learner (DTL), which partitions the space into simplices using Delaunay triangulation and fits linear models within each, and they compared its performance with other learners in numerical studies.
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.