Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the input space is Euclidean, the choice is much more limited for Gaussian processes whose input space is an undirected graph. In this work, we leverage the stochastic partial differential equation characterization of Mat\'ern Gaussian processes - a widely-used model class in the Euclidean setting - to study their analog for undirected graphs. We show that the resulting Gaussian processes inherit various attractive properties of their Euclidean and Riemannian analogs and provide techniques that allow them to be trained using standard methods, such as inducing points. This enables graph Mat\'ern Gaussian processes to be employed in mini-batch and non-conjugate settings, thereby making them more accessible to practitioners and easier to deploy within larger learning frameworks.
翻译:Gausian 进程是学习未知功能的多功能框架, 从而允许人们使用关于其属性的先前信息。 虽然当输入空间为欧洲克利德兰时, 许多不同的高斯进程模型很容易获得, 但对于输入空间为非定向图解的高斯进程来说,选择范围要有限得多。 在这项工作中, 我们利用 Mat\'ern Gaussian 过程的随机偏差部分方程式定性 — — 欧克利德兰环境中广泛使用的模型类 — — 来研究其非定向图形的模拟。 我们显示, 由此产生的高斯进程继承了其欧洲克利德兰和里曼尼模拟模型的各种有吸引力的特性, 并提供了技术, 使其能够通过标准方法( 如导出点) 接受培训。 这样, 图表 Mat\'ern Gaussian 进程就可以在小型批次和非 conjugate 环境中使用, 从而让从业人员更容易接触, 更容易在更大的学习框架内应用。