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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.03263 |
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Table of Contents:
- 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.