Bayesian Neighborhood Adaptation for Graph Neural Networks

The neighborhood scope (i.e., number of hops) where graph neural networks (GNNs) aggregate information to characterize a node's statistical property is critical to GNNs' performance. Two-stage approaches, training and validating GNNs for every pre-specified neighborhood scope to search for the best setting, is a time-consuming task and tends to be biased due to the search space design. How to adaptively determine proper neighborhood scopes for the aggregation process for both homophilic and heterophilic graphs remains largely unexplored. We thus propose to model the GNNs' message-passing behavior on a graph as a stochastic process by treating the number of hops as a beta process. This Bayesian framework allows us to infer the most plausible neighborhood scope for message aggregation simultaneously with the optimization of GNN parameters. Our theoretical analysis shows that the scope inference improves the expressivity of a GNN. Experiments on benchmark homophilic and heterophilic datasets show that the proposed method is compatible with state-of-the-art GNN variants, achieving competitive or superior performance on the node classification task, and providing well-calibrated predictions.

Predicting Biomedical Interactions with Probabilistic Model Selection for Graph Neural Networks

A biological system is a complex network of heterogeneous molecular entities and their interactions contributing to various biological characteristics of the system. However, current biological networks are noisy, sparse, and incomplete, limiting our ability to create a holistic view of the biological system and understand the biological phenomena. Experimental identification of such interactions is both time-consuming and expensive. With the recent advancements in high-throughput data generation and significant improvement in computational power, various computational methods have been developed to predict novel interactions in the noisy network. Recently, deep learning methods such as graph neural networks have shown their effectiveness in modeling graph-structured data and achieved good performance in biomedical interaction prediction. However, graph neural networks-based methods require human expertise and experimentation to design the appropriate complexity of the model and significantly impact the performance of the model. Furthermore, deep graph neural networks face overfitting problems and tend to be poorly calibrated with high confidence on incorrect predictions. To address these challenges, we propose Bayesian model selection for graph convolutional networks to jointly infer the most plausible number of graph convolution layers (depth) warranted by data and perform dropout regularization simultaneously. Experiments on four interaction datasets show that our proposed method achieves accurate and calibrated predictions. Our proposed method enables the graph convolutional networks to dynamically adapt their depths to accommodate an increasing number of interactions.