AUTHOR=Govindarajan Nithin , Vervliet Nico , De Lathauwer Lieven 

TITLE=Regression and Classification With Spline-Based Separable Expansions

JOURNAL=Frontiers in Big Data

VOLUME=5

YEAR=2022

URL=https://www.frontiersin.org/journals/big-data/articles/10.3389/fdata.2022.688496

DOI=10.3389/fdata.2022.688496

ISSN=2624-909X

ABSTRACT=<p>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.</p>