Thanks to graph neural networks (GNNs), semi-supervised node classification has shown the state-of-the-art performance in graph data. However, GNNs have not considered different types of uncertainties associated with the class probabilities to minimize risk increasing misclassification under uncertainty in real life. In this work, we propose a Subjective Bayesian deep learning framework reflecting various types of uncertainties for classification predictions by leveraging the powerful modeling and learning capabilities of GNNs. We considered multiple uncertainty types in both deep learning (DL) and belief/evidence theory domains. We treat the predictions of a Subjective Bayesian GNN (S-BGNN) as nodes' multinomial subjective opinions in a graph based on Dirichlet distributions where each belief mass is a belief probability of each class. By collecting evidence from the given labels of training nodes, the S-BGNN model is designed for accurately predicting probabilities of each class and detecting out-of-distribution. We validated the outperformance of the proposed S-BGNN, compared to the state-of-the-art counterparts in terms of the accuracy of node classification prediction and out-ofdistribution detection based on six real network datasets.
The authors proposed a Bayesian graph neural network framework for node classification. The proposed models outperformed the baselines in six node classification tasks. The main contribution is to evaluate various uncertainty measures for the uncertainty analysis of Bayesian graph neural networks. The authors show that vacuity and aleatoric measure are important to detect out-of-distribution and the dissonance uncertainty plays a key role for improving performance.
** Introduction/Conclusion/Contribution
- Applying MC dropout to graph neural networks is a bit old idea [1-5], it cannot be considered as the “contribution” of this study.
- The authors should emphasize more on what’s the advancements over existing studies.
** Methodology
- My understanding is the authors proposed to use multiple uncertainties (vacuity, dissonance, aleatoric, epstemic). Vacuity and dissonance measures can also be implemented with other Bayesian graph neural networks.
- Ablation study is need to demonstrate the usefulness of each component in the objective function (equation 11). 
- Can “BGAT-T” be considered as the proposed method? It doesn't use the proposed GNN framework but just an extension of original GAT with MC dropout and knowledge distillation.
** Experiments
- Please provide the details of hyperparameter settings, e.g. optimizer, batch size, learning rates, …
- The authors should perform experiments with varying numbers of labels per category (e.g. 5, 10, 20), because different methods show different behaviors under label scarcity.
- There are a number of recently published papers that address node classification based on Bayesian graph neural networks, e.g., see references. They should be used as baselines if available.
- I think the authors should evaluate BGAT-T with Co.Physics, Ama.Computer, and Ama.Photo datasets, because this method was overall superior to other methods on the first three datasets. 
- Experiments are insufficient in the uncertainty analysis (section 5). The authors can evaluate the performance of BGAT as well as other Bayesian graph neural networks in terms of uncertainty quantification performance. 
- Also, in order to evaluate uncertainty quantification performance, I would suggest to look at the trade-off between classification accuracy and classification rejection based on the uncertainty, like accuracy-rejection curve in [6] 
** misc
- Check the following sentence of subsection 3.6. “our key contribution is that the proposed Bayesian GNN model is capable of estimating various uncertainty types to predict existing GNNs.”
References
[1] Ryu, S., Kwon, Y., & Kim, W. Y. (2019). Uncertainty quantification of molecular property prediction with Bayesian neural networks. arXiv preprint arXiv:1903.08375.
[2] Zhang, Y., & Lee, A. A. (2019). Bayesian semi-supervised learning for uncertainty-calibrated prediction of molecular properties and active learning. arXiv preprint arXiv:1902.00925.
[3] Pal, S., Regol, F. L. O. R. E. N. C. E., & Coates, M. A. R. K. (2019). Bayesian graph convolutional neural networks using non-parametric graph learning. In Representation Learning on Graphs and Manifolds Workshop, Int. Conf. Learning Representations.
[4] Akita, H., Nakago, K., Komatsu, T., Sugawara, Y., Maeda, S. I., Baba, Y., & Kashima, H. (2018, December). Bayesgrad: Explaining predictions of graph convolutional networks. In International Conference on Neural Information Processing (pp. 81-92). Springer, Cham.
[5] Zhang, Y., Pal, S., Coates, M., & Ustebay, D. (2019, July). Bayesian graph convolutional neural networks for semi-supervised classification. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 33, pp. 5829-5836).
[6] Nadeem, M. S. A., Zucker, J. D., & Hanczar, B. (2009, March). Accuracy-rejection curves (ARCs) for comparing classification methods with a reject option. In Machine Learning in Systems Biology (pp. 65-81).