In this paper, we first mathematically formulate thetwochallenging problems forgraph data andtake an initiative on tackling them under a unified probabilistic model.

Despite the remarkable success of graph neural networks (GNNs) for graph representation learning, they are generally built on the (unreliable) i.i.d.

Despite the remarkable success of graph neural networks (GNNs) for graph representation learning, they are generally built on the (unreliable) i.i.d.

Despite the remarkable success of graph neural networks (GNNs) for graph representation learning, they are generally built on the (unreliable) i.i.d. However, real-world graph data are universally comprised of outliers in training set and out-of-distribution (OOD) testing samples from unseen domains, which solicits effective models for i) debiased learning and ii) OOD detection, towards general trustworthy purpose. In this paper, we first mathematically formulate the two challenging problems for graph data and take an initiative on tackling them under a unified probabilistic model. Specifically, we model the graph generative process to characterize the distribution shifts of graph data together with an additionally introduced latent environment variable as an indicator. We then define a variational distribution, i.e., a recognition model, to infer the environment during training of GNN.