非渐近快速收敛随机微分方程的非参数学习

IF 2.5 1区 数学 Q2 COMPUTER SCIENCE, THEORY & METHODS
Riccardo Bonalli, Alessandro Rudi
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引用次数: 0

摘要

我们提出了一种新的非参数学习范式,用于识别多维非线性随机微分方程的漂移和扩散系数,该范式依赖于状态的离散时间观测。关键思想本质上是将相应的Fokker-Planck方程的基于rhk的近似拟合到这些观测值中,产生非渐近学习率的理论估计,与以前的工作不同,当未知漂移和扩散系数的规律性变得更高时,理论估计会变得越来越紧密。我们的方法是基于核的,离线预处理可以有效地利用来实现有效的数值实现,在精度和计算复杂性之间提供良好的平衡。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Non-parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence

We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker–Planck equation to such observations, yielding theoretical estimates of non-asymptotic learning rates which, unlike previous works, become increasingly tighter when the regularity of the unknown drift and diffusion coefficients becomes higher. Our method being kernel-based, offline pre-processing may be profitably leveraged to enable efficient numerical implementation, offering excellent balance between precision and computational complexity.

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来源期刊
Foundations of Computational Mathematics
Foundations of Computational Mathematics 数学-计算机:理论方法
CiteScore
6.90
自引率
3.30%
发文量
46
审稿时长
>12 weeks
期刊介绍: Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer. With its distinguished editorial board selecting papers of the highest quality and interest from the international community, FoCM hopes to influence both mathematics and computation. Relevance to applications will not constitute a requirement for the publication of articles. The journal does not accept code for review however authors who have code/data related to the submission should include a weblink to the repository where the data/code is stored.
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