论文标题
基于图形的高斯流程在受限域上
Graph Based Gaussian Processes on Restricted Domains
论文作者
论文摘要
在非参数回归中，输入属于欧几里得空间的受限子集很常见。基于内核的典型方法未考虑收集观测值的域的固有几何形状可能会产生亚最佳结果。在本文中，我们着重于在高斯过程（GP）模型的背景下解决此问题，提出了一类新的基于Laplacian的GPH GPS（GL-GPS），该类别学习尊重输入域几何形状的协方差。由于热核在计算上是棘手的，因此我们使用图形laplacian（GL）有限的特征仪近似协方差。 GL是由仅取决于输入的欧几里得坐标的内核构建的。因此，我们可以从有关内核的全部知识中受益，以将协方差结构扩展到NyStröm型扩展名到新到达的样本。我们为GL-GP方法提供了实质性的理论支持，并说明了各种应用中的性能提高。
In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are collected may produce sub-optimal results. In this article, we focus on solving this problem in the context of Gaussian process (GP) models, proposing a new class of Graph Laplacian based GPs (GL-GPs), which learn a covariance that respects the geometry of the input domain. As the heat kernel is intractable computationally, we approximate the covariance using finitely-many eigenpairs of the Graph Laplacian (GL). The GL is constructed from a kernel which depends only on the Euclidean coordinates of the inputs. Hence, we can benefit from the full knowledge about the kernel to extend the covariance structure to newly arriving samples by a Nyström type extension. We provide substantial theoretical support for the GL-GP methodology, and illustrate performance gains in various applications.
