The issue of distribution shifts is emerging as a critical concern in graph representation learning. From the perspective of invariant learning and stable learning, a recently well-established paradigm for out-of-distribution generalization, stable features of the graph are assumed to causally determine labels, while environmental features tend to be unstable and can lead to the two primary types of distribution shifts. The correlation shift is often caused by the spurious correlation between environmental features and labels that differs between the training and test data; the covariate shift often stems from the presence of new environmental features in test data. However, most strategies, such as invariant learning or graph augmentation, typically struggle with limited training environments or perturbed stable features, thus exposing limitations in handling the problem of covariate shift. To address this challenge, we propose a simple-yet-effective data augmentation strategy, Adversarial Invariant Augmentation (AIA), to handle the covariate shift on graphs. Specifically, given the training data, AIA aims to extrapolate and generate new environments, while concurrently preserving the original stable features during the augmentation process. Such a design equips the graph classification model with an enhanced capability to identify stable features in new environments, thereby effectively tackling the covariate shift in data. Extensive experiments with in-depth empirical analysis demonstrate the superiority of our approach. The implementation codes are publicly available at https://github.com/yongduosui/AIA.

The issue of distribution shifts is emerging as a critical concern in graph representation learning. From the perspective of invariant learning and stable learning, a recently well-established paradigm for out-of-distribution generalization, stable features of the graph are assumed to causally determine labels, while environmental features tend to be unstable and can lead to the two primary types of distribution shifts. The correlation shift is often caused by the spurious correlation between environmental features and labels that differs between the training and test data; the covariate shift often stems from the presence of new environmental features in test data. However, most strategies, such as invariant learning or graph augmentation, typically struggle with limited training environments or perturbed stable features, thus exposing limitations in handling the problem of covariate shift. To address this challenge, we propose a simple-yet-effective data augmentation strategy, Adversarial Invariant Augmentation (AIA), to handle the covariate shift on graphs.

Graphs are ubiquitous in various fields, and deep learning methods have been successful applied in graph classification tasks. However, building large and diverse graph datasets for training can be expensive. While augmentation techniques exist for structured data like images or numerical data, the augmentation of graph data remains challenging. This is primarily due to the complex and non-Euclidean nature of graph data. In this paper, it has been proposed a novel augmentation strategy for graphs that operates in a non-Euclidean space. This approach leverages graphon estimation, which models the generative mechanism of networks sequences. Computational results demonstrate the effectiveness of the proposed augmentation framework in improving the performance of graph classification models. Additionally, using a non-Euclidean distance, specifically the Gromow-Wasserstein distance, results in better approximations of the graphon. This framework also provides a means to validate different graphon estimation approaches, particularly in real-world scenarios where the true graphon is unknown.

Self-supervised learning and pre-training strategies have developed over the last few years especially for Convolutional Neural Networks (CNNs). Recently application of such methods can also be noticed for Graph Neural Networks (GNNs). In this paper, we have used a graph based self-supervised learning strategy with different loss functions (Barlow Twins[ 7], HSIC[ 4], VICReg[ 1]) which have shown promising results when applied with CNNs previously. We have also proposed a hybrid loss function combining the advantages of VICReg and HSIC and called it as VICRegHSIC. The performance of these aforementioned methods have been compared when applied to two different datasets namely MUTAG and PROTEINS. Moreover, the impact of different batch sizes, projector dimensions and data augmentation strategies have also been explored. The results are preliminary and we will be continuing to explore with other datasets.