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.

Code description

This package provides the implementation of the regression and classification technique employing splines in combination with sums of separable functions. Experiment files included reproduce all the results of the paper.

Reference

N. Govindarajan, N. Vervliet, and L. De Lathauwer. "Regression and classification with spline-based separable expansions." Frontiers in Big Data, vol. 5, 2022.

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