Delaunay-Triangulation-Based Learning with Hessian Total-Variation Regularization

Regression is one of the core problems tackled in supervised learning. Neural networks with rectified linear units generate continuous and piecewise-linear (CPWL) mappings are state-of-the-art approach for solving regression problems. In this paper, we propose an alternative method that leverages expressivity CPWL functions. contrast to deep neural networks, our parameterization guarantees stability interpretable. Our relies on partitioning domain function by a Delaunay triangulation. The values at vertices triangulation learnable parameters identify uniquely. Formulating learning scheme as variational problem, use Hessian total variation (HTV) regularizer favor functions few affine pieces. way, control complexity model through single hyperparameter. By developing computational framework compute HTV any parameterized triangulation, discretize problem generalized least absolute shrinkage selection operator. experiments validate usage low-dimensional scenarios.