几何核包：用于流形、网格和图上几何学习的热核和Matérn核
The GeometricKernels Package: Heat and Matérn Kernels for Geometric Learning on Manifolds, Meshes, and Graphs
AI总结：
GeometricKernels 是一个用于几何学习的Python包，实现了热核和Matérn核，支持在流形、网格和图上进行不确定性量化和自动微分。
摘要：
核是机器学习中的基本技术原语。近年来，基于核的方法，如高斯过程，在需要量化不确定性的重要应用中变得越来越重要。在涉及在图、网格、流形或其他相关空间上定义的结构化数据的设置中，定义具有良好不确定性量化行为的核，并计算其数值值，比在欧几里得设置中要更不直接。为了解决这个困难，我们提出了GeometricKernels，一个Python软件包，实现了经典的欧几里得平方指数——也称为热——和Matérn核的几何类比，这些核广泛用于不确定性至关重要的设置中。作为副产品，我们获得了在广泛几何空间上计算傅里叶特征类型展开的能力，这些展开在它们自己的权利上被广泛使用。我们的实现通过后端无关的设计，在所有主要当前框架中支持自动微分。在该软件包及其文档的配套论文中，我们概述了该包的能力，并展示了其接口的示例。我们还简要概述了该包所基于的理论，并在附录中提供了一些历史背景。
英文摘要：
Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-based methods such as Gaussian processes are becoming increasingly important in applications where quantifying uncertainty is of key interest. In settings that involve structured data defined on graphs, meshes, manifolds, or other related spaces, defining kernels with good uncertainty-quantification behavior, and computing their value numerically, is less straightforward than in the Euclidean setting. To address this difficulty, we present GeometricKernels, a Python software package which implements the geometric analogs of classical Euclidean squared exponential - also known as heat - and Matérn kernels, which are widely-used in settings where uncertainty is of key interest. As a byproduct, we obtain the ability to compute Fourier-feature-type expansions, which are widely used in their own right, on a wide set of geometric spaces. Our implementation supports automatic differentiation in every major current framework simultaneously via a backend-agnostic design. In this companion paper to the package and its documentation, we outline the capabilities of the package and present an illustrated example of its interface. We also include a brief overview of the theory the package is built upon and provide some historic context in the appendix.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
