Evolving Graph Learning for Out-of-Distribution Generalization in Non-stationary Environments

TL;DR

This work tackles out-of-distribution generalization in dynamic graphs by introducing EvoGOOD, which models evolving environments with an Environment Sequential Variational Autoencoder (ESVAE) and learns environment-aware invariant patterns. It combines a spatio-temporal graph encoder, node-wise masks to separate invariant from variant features, and a node-level causal intervention mechanism that uses both observed and generated environment samples to improve robustness under non-stationary shifts. The authors provide theoretical assurances for invariance and an upper bound on OOD error, and demonstrate state-of-the-art performance on future link prediction and node classification across real-world and synthetic datasets. By framing dynamic graph generation as evolving environments and enabling fine-grained interventions, EvoGOOD advances OOD generalization in non-stationary settings with practical implications for robust graph learning.

Abstract

Graph neural networks have shown remarkable success in exploiting the spatial and temporal patterns on dynamic graphs. However, existing GNNs exhibit poor generalization ability under distribution shifts, which is inevitable in dynamic scenarios. As dynamic graph generation progresses amid evolving latent non-stationary environments, it is imperative to explore their effects on out-of-distribution (OOD) generalization. This paper proposes a novel Evolving Graph Learning framework for OOD generalization (EvoOOD) by environment-aware invariant pattern recognition. Specifically, we first design an environment sequential variational auto-encoder to model environment evolution and infer the underlying environment distribution. Then, we introduce a mechanism for environment-aware invariant pattern recognition, tailored to address environmental diversification through inferred distributions. Finally, we conduct fine-grained causal interventions on individual nodes using a mixture of instantiated environment samples. This approach helps to distinguish spatio-temporal invariant patterns for OOD prediction, especially in non-stationary environments. Experimental results demonstrate the superiority of EvoGOOD on both real-world and synthetic dynamic datasets under distribution shifts. To the best of our knowledge, it is the first attempt to study the dynamic graph OOD generalization problem from the environment evolution perspective.

Figures (6)

• Figure 1: SCM models for graph OOD generalization.
• Figure 2: The framework of EvoGOOD. EvoGOOD is following an environment “Modeling-Inferring-Discriminating-Generalizing” paradigm. Step ①: For a dynamic graph, we first use a spatio-temporal graph attention encoding mechanism to generate node encodings $\{\mathbf{H}^1,\mathbf{H}^2,\cdots,\mathbf{H}^T\}$ and model the latent environments $\mathbf{e}$ (Section \ref{['subsec:graph_encoding']}). Step ②: The environment sequential auto-encoder (ESVAE) learns the environment evolution and then infers the future environment distribution (Section \ref{['subsec:ESVAE']}). Step ③: The environment-aware invariant pattern recognition mechanism $\mathbb{I}(\cdot)$ recognizes the spatio-temporal invariant patterns $\mathcal{P}_I^t$ and variant patterns $\mathcal{P}_V^t$ within the environment for stable predictions (Section \ref{['subsec:invariant_recognition']}).Step ④: Finally, EvoGOOD performs node-wise fine-grained causal interventions with sampled and generative environment instances $\mathcal{S}_{\mathrm{ob}}$ and $\mathcal{S}_{\mathrm{ge}}$ to generalize to non-stationary environments (Section \ref{['subsec:intervention']}).
• Figure 3: Additional analysis of the performance.
• Figure 4: Performance analysis of EvoGOOD.
• Figure 5: Investigation on Environment-aware Invariant Pattern Recognition.

Theorems & Definitions (8)

• Proposition 1
• Proposition 2
• proof
• Lemma 1
• Proposition 3
• proof
• Lemma 2
• proof