论文标题
通过光谱内核学习在图表上的高斯过程
Gaussian Processes on Graphs via Spectral Kernel Learning
论文作者
论文摘要
我们提出了一个基于图频谱的高斯过程，以预测图表节点上定义的信号。该模型旨在通过高度自适应的内核捕获各种图形信号结构，该核在图谱谱域中融合了柔性多项式函数。与大多数现有方法不同，我们建议学习这样的光谱内核，在这种情况下，多项式设置可以学习，而无需图形laplacian的特征分解。此外，该内核具有通过定制的最大似然学习算法实现频谱阳性的定制最大似然学习算法来实现的图形滤波。我们证明了该模型在合成实验中的解释性，从中我们可以准确地恢复各种地面真实光谱过滤器，并且适应性转化为在预测各种特征的现实图形数据中的出色性能。
We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible polynomial function in the graph spectral domain. Unlike most existing approaches, we propose to learn such a spectral kernel, where the polynomial setup enables learning without the need for eigen-decomposition of the graph Laplacian. In addition, this kernel has the interpretability of graph filtering achieved by a bespoke maximum likelihood learning algorithm that enforces the positivity of the spectrum. We demonstrate the interpretability of the model in synthetic experiments from which we show the various ground truth spectral filters can be accurately recovered, and the adaptability translates to superior performances in the prediction of real-world graph data of various characteristics.
