论文标题
Matérn高斯流程图
Matérn Gaussian Processes on Graphs
论文作者
论文摘要
高斯流程是学习未知功能的多功能框架，允许人们利用有关其属性的先前信息。尽管当输入空间为欧几里得时，许多不同的高斯工艺模型很容易获得，但对于高斯流程的选择，其输入空间是无方向的图，选择的限制要受到更大的限制。在这项工作中，我们利用Matérn高斯过程的随机部分微分方程表征（欧几里得环境中广泛使用的模型类）来研究其对无向图的类似物。我们表明，所得的高斯工艺继承了其欧几里得和里曼尼亚类似物的各种有吸引力的特性，并提供了可以使用标准方法（例如诱导点）训练它们的技术。这使图形Matérn高斯流程可以在迷你批次和非偶联设置中使用，从而使从业者更容易访问它们，并且更易于在较大的学习框架内部署。
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 Matérn 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 Matérn 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.
