# Fitting scattered data with optional monotonicity constraints on GPU: LipFit package

arXiv: https://arxiv.org/abs/2606.04670 · HTML: https://mlsanity.com/paper/2606.04670/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 37 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 7 of 7)

- [Certified Monotonic Neural Networks](https://mlsanity.com/paper/2011.10219/) (2020)
- [Testing Monotonicity of Machine Learning Models](https://mlsanity.com/paper/2002.12278/) (2020)
- [Approximation, characterization, and continuity of multivariate monotonic regression functions](https://mlsanity.com/paper/2009.02317/) (2020)
- [MonoKAN: Certified Monotonic Kolmogorov-Arnold Network](https://mlsanity.com/paper/2409.11078/) (2024)
- [Twin Neural Network Improved k-Nearest Neighbor Regression](https://mlsanity.com/paper/2310.00664/) (2023)
- [Active Nearest Neighbor Regression Through Delaunay Refinement](https://mlsanity.com/paper/2206.08061/) (2022)
- [From Isotonic to Lipschitz Regression: A New Interpolative Perspective on Shape-restricted Estimation](https://mlsanity.com/paper/2307.05732/) (2023)

## 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.