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arXiv · 2504.03263

Non-parametric B-spline decoupling of multivariate functions

Joppe De Jonghe·Mariya Ishteva
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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.

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Joppe De Jonghe, Mariya Ishteva. 2025-04-04. Non-parametric B-spline decoupling of multivariate functions. https://arxiv.org/abs/2504.03263

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