Non-parametric B-spline decoupling of multivariate functions
Abstract
Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear transformations and nonlinear univariate functions. This work introduces an efficient decoupling algorithm that leverages the use of B-splines to allow a non-parametric estimation of the decoupling's internal functions. The use of B-splines alleviates the problem of choosing an appropriate basis, as in parametric methods, but still allows an intuitive way to tweak the flexibility of the estimated functions. Besides the non-parametric property, the use of B-spline representations allows for easy integration of nonnegativity or monotonicity constraints on the function shapes, which is not possible for the currently available (non-)parametric decoupling methods. The proposed algorithm is illustrated on synthetic examples that highlight the flexibility of the B-spline representation and the ease with which a monotonicity constraint can be added. The examples also show that if monotonic functions are required, enforcing the constraint is necessary.
Cite
@article{arxiv.2504.03263,
title = {Non-parametric B-spline decoupling of multivariate functions},
author = {Joppe De Jonghe and Mariya Ishteva},
journal= {arXiv preprint arXiv:2504.03263},
year = {2025}
}