Fitting scattered data with optional monotonicity constraints on GPU: LipFit package
2026-06-03 • Machine Learning
Machine LearningMathematical Software
AI summaryⓘ
The authors introduce a way to guess missing or scattered data points while making sure the guess is smooth and follows certain increasing or decreasing rules. Their method is like finding the closest known points but avoids sudden jumps in the results. They also show how to make these guesses smoother and how to run the method quickly using GPUs. The authors provide a Python package called LipFit that users can use to apply these techniques without needing to train a model first.
multivariate interpolationLipschitz continuitymonotonicity constraintsnearest-neighbour approximationGPU parallelisationlocal interpolationinstance-based approximationscattered dataPython package
Authors
Gleb Beliakov
Abstract
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.