Unifying Invariant and Variant Features for Graph Out-of-Distribution via Probability of Necessity and Sufficiency

TL;DR

This paper introduces a novel graph learning method that combines invariant and variant features using probability of necessity and sufficiency to improve out-of-distribution generalization, outperforming existing techniques.

Contribution

It proposes a theoretical framework and a practical model, SNIGL, that effectively extracts invariant subgraphs and leverages domain-specific variants for better generalization.

Findings

SNIGL outperforms state-of-the-art methods on six benchmarks.

Theoretical bounds enable effective extraction of invariant subgraphs.

Ensemble of invariant and variant classifiers enhances generalization.

Abstract

Graph Out-of-Distribution (OOD), requiring that models trained on biased data generalize to the unseen test data, has considerable real-world applications. One of the most mainstream methods is to extract the invariant subgraph by aligning the original and augmented data with the help of environment augmentation. However, these solutions might lead to the loss or redundancy of semantic subgraphs and result in suboptimal generalization. To address this challenge, we propose exploiting Probability of Necessity and Sufficiency (PNS) to extract sufficient and necessary invariant substructures. Beyond that, we further leverage the domain variant subgraphs related to the labels to boost the generalization performance in an ensemble manner. Specifically, we first consider the data generation process for graph data. Under mild conditions, we show that the sufficient and necessary invariant subgraph can be extracted by minimizing an upper bound, built on the theoretical advance of the probability of necessity and sufficiency. To further bridge the theory and algorithm, we devise the model called Sufficiency and Necessity Inspired Graph Learning (SNIGL), which ensembles an invariant subgraph classifier on top of latent sufficient and necessary invariant subgraphs, and a domain variant subgraph classifier specific to the test domain for generalization enhancement. Experimental results demonstrate that our SNIGL model outperforms the state-of-the-art techniques on six public benchmarks, highlighting its effectiveness in real-world scenarios.