This paper introduces a novel and generic framework to solve the flagship task of supervised labeled graph prediction by leveraging Optimal Transport tools. We formulate the problem as regression with the Fused Gromov-Wasserstein (FGW) loss and propose a predictive model relying on a FGW barycenter whose weights depend on inputs. First we introduce a non-parametric estimator based on kernel ridge regression for which theoretical results such as consistency and excess risk bound are proved. Next we propose an interpretable parametric model where the barycenter weights are modeled with a neural network and the graphs on which the FGW barycenter is calculated are additionally learned. Numerical experiments show the strength of the method and its ability to interpolate in the labeled graph space on simulated data and on a difficult metabolic identification problem where it can reach very good performance with very little engineering.

翻译：本文引入了一个新的通用框架, 以利用最佳运输工具解决有监督标签的图表预测的旗舰任务。 我们用Fuse Gromov-Wasserstein(FGW)损失将问题表述为回归问题, 并提议一个依赖其重量依赖于投入的FGW 嘉宾中心的预测模型。 首先, 我们引入了一个基于内核脊回归的非参数估测器, 其理论结果如一致性和超重风险捆绑。 下一步, 我们提出一个可解释的参数模型, 该模型将恒温器重量与神经网络建模, 以及计算FGW Barycenter(FGW) 的图表是额外学习的。 数值实验显示了该方法的强度及其在模拟数据标注的图形空间内进行干涉的能力, 以及一个难以解释的代谢识别问题, 在那里, 它能以很少的工程技术达到非常良好的性能。