Regression and Classification With Spline-Based Separable Expansions

Abstract

We introduce a supervised learning framework for target functions that are well approximated by a sum of (few) separable terms. The framework proposes to approximate each component function by a B-spline, resulting in an approximant where the underlying coefficient tensor of the tensor product expansion has a low-rank polyadic decomposition parametrization. By exploiting the multilinear structure, as well as the sparsity pattern of the compactly supported B-spline basis terms, we demonstrate how such an approximant is well-suited for regression and classification tasks by using the Gauss-Newton algorithm to train the parameters. Various numerical examples are provided analyzing the effectiveness of the approach.

Keywords: B-splines; canonical polyadic decomposition; classification; gauss-newton; regression; supervised learning; tensor decompositions.