Pave Your Own Path: Graph Gradual Domain Adaptation on Fused Gromov-Wasserstein Geodesics

TL;DR

This work addresses the challenge of large distribution shifts in graph neural networks by proposing Gadget, the first graph gradual domain adaptation framework for non-IID graphs. Gadget leverages Fused Gromov-Wasserstein (FGW) distances to quantify domain discrepancy and proves that the optimal gradual path lies along FGW geodesics, minimizing the target error as the adaptation proceeds along intermediate graphs. A practical path-generation module uses low-rank optimal transport to align source and target graphs and interpolate along FGW geodesics, while an entropy-based confidence mechanism enhances self-training for pseudo-labels. The approach yields consistent gains over direct adaptation across real and synthetic datasets and provides insights into the geodesic structure of graph shifts, enabling scalable and effective large-shift graph DA.

Abstract

Graph neural networks, despite their impressive performance, are highly vulnerable to distribution shifts on graphs. Existing graph domain adaptation (graph DA) methods often implicitly assume a \textit{mild} shift between source and target graphs, limiting their applicability to real-world scenarios with \textit{large} shifts. Gradual domain adaptation (GDA) has emerged as a promising approach for addressing large shifts by gradually adapting the source model to the target domain via a path of unlabeled intermediate domains. Existing GDA methods exclusively focus on independent and identically distributed (IID) data with a predefined path, leaving their extension to \textit{non-IID graphs without a given path} an open challenge. To bridge this gap, we present Gadget, the first GDA framework for non-IID graph data. First (\textit{theoretical foundation}), the Fused Gromov-Wasserstein (FGW) distance is adopted as the domain discrepancy for non-IID graphs, based on which, we derive an error bound revealing that the target domain error is proportional to the length of the path. Second (\textit{optimal path}), guided by the error bound, we identify the FGW geodesic as the optimal path, which can be efficiently generated by our proposed algorithm. The generated path can be seamlessly integrated with existing graph DA methods to handle large shifts on graphs, improving state-of-the-art graph DA methods by up to 6.8\% in node classification accuracy on real-world datasets.

Figures (10)

• Figure 1: An illustration of graph GDA. Figures (a-b) show the node embeddings, whose colors (blue and red) indicate classes and shapes ($\bullet$ and $\times$) indicate domains, and the decision boundary. (a): Direct adaptation fails when facing large shifts as all target nodes in class 0 ($\times$) are misclassified. (b): Gradual adaptation successfully handles large shift by decomposing it into intermediate domains on the FGW geodesics with mild shifts, where all target nodes in class 0 ($\times$) are correctly separated from those in class 1 ($\times$). (c): Bars w/ and w/o hatches show the performance of direct adaptation and GDA, respectively. Number over bars are the absolute improvement on accuracy. Our proposed Gadget significantly improves various graph DA methods on real-world datasets.
• Figure 2: Experiment results. Different colors indicate different baseline adaptation methods. Bars with and without hatches indicate direct adaptation and gradual adaptation with Gadget, respectively. Our proposed Gadget consistently achieves better performance than direct adaptation on different backbone GNNs, adaptation methods and datasets. Best viewed in color.
• Figure 3: Embedding space of CSBM dataset under homophily shifts. Direct adaptation (left) fails when facing large shifts. GDA (right) correctly classifies most samples in each step, resulting in significant improvement in the classification accuracy. Best viewed in color.
• Figure 4: Experiment analysis. (a) Geodesic property: each scatter represents two graphs $\gamma(\lambda_0),\gamma(\lambda_1)$; (b) Performance against different shift levels; (c) Performance with different rank $r$; (d) Performance with different intermediate steps $T$.
• Figure 5: Node classification accuracy under different levels.

Theorems & Definitions (19)

• Definition 1: FGW distance: peyre2016gromovpeyre2019computationaltitouan2019optimal
• Definition 2: FGW equivalence class
• Definition 3: FGW geodesic
• Definition 4: Unsupervised graph DA
• Definition 5: Path
• Definition 6: Graph gradual domain adaptation
• Definition 7: Graph convolution
• Lemma 1: Hölder continuity
• Theorem 1: Error bound
• Theorem 2: Optimal path