# Bayesian Graph Neural Networks with Adaptive Connection Sampling

arXiv: https://arxiv.org/abs/2006.04064 · HTML: https://mlsanity.com/paper/2006.04064/

## Key facts

- Cited by 81 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2020.

## Built on by (most cited first, 30 of 81)

- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Training Graph Neural Networks with 1000 Layers](https://mlsanity.com/paper/2106.07476/) (2021)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [Decoupling the Depth and Scope of Graph Neural Networks](https://mlsanity.com/paper/2201.07858/) (2022)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Demystifying Oversmoothing in Attention-Based Graph Neural Networks](https://mlsanity.com/paper/2305.16102/) (2023)
- [Sampling methods for efficient training of graph convolutional networks: A survey](https://mlsanity.com/paper/2103.05872/) (2021)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [Confidence May Cheat: Self-Training on Graph Neural Networks under Distribution Shift](https://mlsanity.com/paper/2201.11349/) (2022)
- [Bag of Tricks for Training Deeper Graph Neural Networks: A Comprehensive Benchmark Study](https://mlsanity.com/paper/2108.10521/) (2021)
- [Class-Imbalanced Graph Learning without Class Rebalancing](https://mlsanity.com/paper/2308.14181/) (2023)
- [Distribution Free Prediction Sets for Node Classification](https://mlsanity.com/paper/2211.14555/) (2022)
- [Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching](https://mlsanity.com/paper/2312.16560/) (2023)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [A Survey of Trustworthy Graph Learning: Reliability, Explainability, and Privacy Protection](https://mlsanity.com/paper/2205.10014/) (2022)
- [Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learning](https://mlsanity.com/paper/2505.15547/) (2025)
- [Graph Classification by Mixture of Diverse Experts](https://mlsanity.com/paper/2103.15622/) (2021)
- [JuryGCN: Quantifying Jackknife Uncertainty on Graph Convolutional Networks](https://mlsanity.com/paper/2210.05959/) (2022)
- [A General Framework for quantifying Aleatoric and Epistemic uncertainty in Graph Neural Networks](https://mlsanity.com/paper/2205.09968/) (2022)
- [Robust Node Classification on Graphs: Jointly from Bayesian Label Transition and Topology-based Label Propagation](https://mlsanity.com/paper/2208.09779/) (2022)
- [Safety in Graph Machine Learning: Threats and Safeguards](https://mlsanity.com/paper/2405.11034/) (2024)
- [Recent Advances in Reliable Deep Graph Learning: Inherent Noise, Distribution Shift, and Adversarial Attack](https://mlsanity.com/paper/2202.07114/) (2022)
- [Retention Time Prediction for Chromatographic Enantioseparation by Quantile Geometry-enhanced Graph Neural Network](https://mlsanity.com/paper/2211.03602/) (2022)
- [Accurate and Scalable Estimation of Epistemic Uncertainty for Graph Neural Networks](https://mlsanity.com/paper/2401.03350/) (2024)
- [Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equations](https://mlsanity.com/paper/2408.16115/) (2024)
- [TyXe: Pyro-based Bayesian neural nets for Pytorch](https://mlsanity.com/paper/2110.00276/) (2021)
- [A Graph Is More Than Its Nodes: Towards Structured Uncertainty-Aware Learning on Graphs](https://mlsanity.com/paper/2210.15575/) (2022)
- [Sparsification and Filtering for Spatial-temporal GNN in Multivariate Time-series](https://mlsanity.com/paper/2203.03991/) (2022)

## Abstract (arXiv)

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.