  We propose a unified framework for adaptive connection sampling in graph
neural networks (GNNs) that generalizes existing stochastic regularization
methods for training GNNs. The proposed framework not only alleviates
over-smoothing and over-fitting tendencies of deep GNNs, but also enables
learning with uncertainty in graph analytic tasks with GNNs. Instead of using
fixed sampling rates or hand-tuning them as model hyperparameters in existing
stochastic regularization methods, our adaptive connection sampling can be
trained jointly with GNN model parameters in both global and local fashions.
GNN training with adaptive connection sampling is shown to be mathematically
equivalent to an efficient approximation of training Bayesian GNNs.
Experimental results with ablation studies on benchmark datasets validate that
adaptively learning the sampling rate given graph training data is the key to
boost the performance of GNNs in semi-supervised node classification, less
prone to over-smoothing and over-fitting with more robust prediction.
