Fitting scattered data with optional monotonicity constraints on GPU: LipFit package
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Abstract (arXiv)
This paper presents a method of multivariate scattered data interpolation and approximation that produces optimal Lipschitz-continuous approximation, subject to the desired monotonicity constraints. This method relies on tight upper and lower approximations to the data, and is similar in its spirit to the nearest-neighbour approximation but does not suffer from discontinuities. Local Lipschitz interpolation and Lipschitz smoothing are also presented. This approach falls under the umbrella of instance-based approximation with no training phase, and it is suitable for GPU-based parallelisation. A Python GPU-friendly package LipFit which implements the methods discussed is discussed.
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References · 7
- 2020Certified Monotonic Neural Networkscited by 51
- 2020Testing Monotonicity of Machine Learning Modelscited by 8
- 2020Approximation, characterization, and continuity of multivariate monotonic regression functionscited by 4
- 2024MonoKAN: Certified Monotonic Kolmogorov-Arnold Networkcited by 4
- 2023Twin Neural Network Improved k-Nearest Neighbor Regressioncited by 2
- 2022Active Nearest Neighbor Regression Through Delaunay Refinementcited by 1
- 2023From Isotonic to Lipschitz Regression: A New Interpolative Perspective on Shape-restricted Estimationcited by 1
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