We propose a novel Bayesian nonparametric method to learn
translation-invariant relationships on non-Euclidean domains. The resulting
graph convolutional Gaussian processes can be applied to problems in machine
learning for which the input observations are functions with domains on general
graphs. The structure of these models allows for high dimensional inputs while
retaining expressibility, as is the case with convolutional neural networks. We
present applications of graph convolutional Gaussian processes to images and
triangular meshes, demonstrating their versatility and effectiveness, comparing
favorably to existing methods, despite being relatively simple models.

提出了一种新的贝叶斯非参数方法，以在非欧几里德域上学习平移不变的关系。 该方法可应用于机器学习问题，其中输入观测值是具有普通图形域的函数。 并将图卷积高斯过程应用于图像和三角形网格等领域，表明了其多功能性和有效性，与现有方法相比具有优势，尽管是相对简单的模型。

图卷积高斯过程

Graph Convolutional Gaussian Processes

We study the problem of estimating the continuous response over time to
interventions using observational time series---a retrospective dataset where
the policy by which the data are generated is unknown to the learner. We are
motivated by applications where response varies by individuals and therefore,
estimating responses at the individual-level is valuable for personalizing
decision-making. We refer to this as the problem of estimating individualized
treatment response (ITR) curves. In statistics, G-computation formula (Robins,
1986) has been commonly used for estimating treatment responses from
observational data containing sequential treatment assignments. However, past
studies have focused predominantly on obtaining point-in-time estimates at the
population level. We leverage the G-computation formula and develop a novel
Bayesian nonparametric (BNP) method that can flexibly model functional data and
provide posterior inference over the treatment response curves at both the
individual and population level. On a challenging dataset containing time
series from patients admitted to a hospital, we estimate responses to
treatments used in managing kidney function and show that the resulting fits
are more accurate than alternative approaches. Accurate methods for obtaining
ITRs from observational data can dramatically accelerate the pace at which
personalized treatment plans become possible.

使用贝叶斯非参数方法来建立个体化治疗反应曲线，从而提升个性化决策的精度，该方法使用观测时间序列，并结合 G - 计算公式对连续响应进行估计。