论文标题
部分可观测时空混沌系统的无模型预测
Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters
论文作者
论文摘要
本文介绍了一个新颖而通用的框架，以利用最佳运输工具来解决监督标记的图形预测的旗舰任务。我们将问题提出为融合Gromov-Wasserstein（FGW）损失的回归，并提出了一个依靠FGW Barycenter的预测模型，该模型依赖于输入。首先，我们基于内核脊回归引入了一个非参数估计器，该估计量证明了一致性和过量风险结合等理论结果。接下来，我们提出了一个可解释的参数模型，其中重心权重以神经网络建模，并进一步学习了FGW Barycenter的图形。数值实验表明了该方法的强度及其在模拟数据上标记的图形空间和困难的代谢识别问题上插值的能力，而工程学很少的工程能够达到非常好的性能。
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.
