超图上的高斯过程
Gaussian Processes on Hypergraphs
摘要：
我们在超图的顶点上导出一个Matern高斯过程（GP）.这使得能够估计与顶点相关联的观测值或潜在值的回归模型，其中相关性和不确定性估计由超图结构通知。我们进一步提出了一个框架，用于嵌入超图的顶点到一个潜在的空间使用超图GP。最后，我们提供了一个方案，用于确定少量的代表性诱导顶点，使可扩展的推理，通过稀疏GP。我们证明了我们的框架的实用性，在三个具有挑战性的现实世界中的问题，涉及多类分类的立法者的政党归属的投票行为的基础上，概率矩阵分解的电影评论，并嵌入到一个低维的潜在空间的动物超图。
英文摘要：
We derive a Matern Gaussian process (GP) on the vertices of a hypergraph. This enables estimation of regression models of observed or latent values associated with the vertices, in which the correlation and uncertainty estimates are informed by the hypergraph structure. We further present a framework for embedding the vertices of a hypergraph into a latent space using the hypergraph GP. Finally, we provide a scheme for identifying a small number of representative inducing vertices that enables scalable inference through sparse GPs. We demonstrate the utility of our framework on three challenging real-world problems that concern multi-class classification for the political party affiliation of legislators on the basis of voting behaviour, probabilistic matrix factorisation of movie reviews, and embedding a hypergraph of animals into a low-dimensional latent space.
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