用GPU加速的LipFit包实现带单调性约束的散点数据拟合
Fitting scattered data with optional monotonicity constraints on GPU: LipFit package
- 基于紧致上下界逼近，生成最优Lipschitz连续插值
- 支持单调性约束，避免传统最近邻法的不连续问题
- 无需训练，适合GPU并行，开源Python包已发布
本文提出一种多变量散点数据插值与逼近方法，可生成满足指定单调性约束的最优Lipschitz连续近似。该方法依赖于对数据的紧致上下界逼近，其思想类似最近邻法，但避免了不连续性问题。文中还介绍了局部Lipschitz插值与Lipschitz平滑技术。该方法属于无训练阶段的实例基础逼近，适用于GPU并行计算。本文还介绍了实现这些方法的Python GPU友好型工具包LipFit。
原文摘要 · Abstract (English)
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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