Outlier-Robust Gromov-Wasserstein for Graph Data

Published: 21 Sept 2023, Last Modified: 15 Jan 2024NeurIPS 2023 spotlightEveryoneRevisionsBibTeX
Keywords: Gromov Wasserstein, Robust Optimization, Nonconvex Optimization
Abstract: Gromov-Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. Recently, GW has become the main modeling technique for aligning heterogeneous data for a wide range of graph learning tasks. However, the GW distance is known to be highly sensitive to outliers, which can result in large inaccuracies if the outliers are given the same weight as other samples in the objective function. To mitigate this issue, we introduce a new and robust version of the GW distance called RGW. RGW features optimistically perturbed marginal constraints within a Kullback-Leibler divergence-based ambiguity set. To make the benefits of RGW more accessible in practice, we develop a computationally efficient and theoretically provable procedure using Bregman proximal alternating linearized minimization algorithm. Through extensive experimentation, we validate our theoretical results and demonstrate the effectiveness of RGW on real-world graph learning tasks, such as subgraph matching and partial shape correspondence.
Supplementary Material: zip
Submission Number: 7296
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