This work employs techniques developed in network science literature, such as latent space model (LSM) and stochastic block model (SBM), to propose a generative model for features X, outputs Y, and graph G, and it uses graph neural networks to approximate the posterior of missing outputs given X, observed Y, and G. This work is a wise combination of recent methods to effectively address the problem of graph-based semi-supervised learning. However, I have some concerns, which are summarized as follows: - Although the paper proposed a new interesting generative method for graph-based semi-supervised learning, it is not super novel, as it employs the other existing methods as the blocks of their method, like LSM, SBM, GCN, GAT. - It seems the generative model is only generative for G given X and Y and by factorizing the other part as p(Y,X) = p(Y|X) p(X), for p(Y|X), it is modeled via a multi-layer perceptron, which is a discriminative model. That is why the authors discard X in all the analyses, like any other discriminative model, and say that everything is conditioned on X. I think this makes the proposed model not fully generative. It is only generative for G but not for X and Y. I was wondering what would be the performance if you would assume p(G,Y,X) = p(G|X,Y) p(X|Y) p(Y), which makes the features X generative conditioned on the outputs? - It is not clarified how the parameters are learned from the ELBO. For example, in SBM, are p_0 and p_1 the only learnable parameters? If yes, how the constraints are taken into account? - Regarding the approximate posterior model, in part 3.3.2, the authors have used graph neural networks to approximate the posterior of missing Y given X, observed Y, and G. However, as mentioned in the paper, graph neural networks get only X and G as input but not any Y. It seems this is not a reasonable approximation as it is not consistent with the graph generation step, LSM and SBM, which use the label information to generate the graphs. What is the reasoning of using graph neural networks? Could you revise them to handle the labels too, which will make the approximation more realistic? - Having mediocre performance on Pubmed data might cast a doubt on dependence of the performance of the proposed method on the input data. How could you explain the poor performance on that dataset? Is there other datasets to test on to prove the efficacy of the proposed method?

Originality: The paper appears to be original. Quality: Good empirical results. It is reassuring that multiple instantiations of the model perform well and very valuable to show these results for different variations. Clarity: This paper is very clearly written and has excellent organisation. Significance: The authors provided a "simple" (yet powerful) implementation of their model, that is competitive with baseline models and may be a strong foundation for future work.

Originality – The proposed generative framework seems reasonable and new for graph-based semi-supervised learning. Quality – The proposed model still relies on GCN/GAT as inference models, and the experimental results only show marginal improvements over GCN/GAT on normal classification tasks. I find the experiments less convincing, and my main concerns are as follows. - 1. Experimental results should be compared against other generative models mentioned in section 2.3, especially Bayesian GCN [22], while the authors only make comparisons to the vanilla GCN/GAT. - 2. I am not sure the missing-edge setting (lines 248-253) is reasonable. The authors say they consider an “extreme” setting by removing all the edges of the test nodes from the graph. Since test nodes are the majority (> 95% in the experiments), after removing the edges connected to them, nearly no edges are left in the training set. How is it possible to train the graph model in this situation? Is it fair for GCN/GAT? Please correct me if I am wrong. - 3. The authors use a validation set with many labels to choose network hyperparameters and the balancing parameter \eta in the overall loss function and for early stopping. This contradicts with the label-scarce setting and is impractical. In fact, GCN/GAT can work reasonably well without using the validation set, albeit with a little performance drop. Bayesian GCN [22] also did not use the validation set. The experimental results would be more convincing if the validation set is not used for searching \eta and early stopping. Clarity – This paper is easy to follow and largely well written, but I think there is still room for improvement in writing and presentation. The notations should be kept consistent throughout the paper, e.g., the notation G of the graph is sometimes in bold and sometimes not. Significance – The proposed model still relies on GCN/GAT as inference models, and I don’t see a clear advantage of the proposed model over GCN/GAT except in the missing-edge setting, but this setting, as described in the paper, does not look reasonable or realistic to me. --------------------------------- After Rebuttal ------------------------------------------------------ I would like to thank the authors for their response. I have read their response and gone through the paper again carefully. I still have the following concerns. -1. Thanks for the explanation, now I understand the setup of the missing-edge experiment. But I still do not understand why the proposed method (GenGNN) would outperform GCN/GAT in this setting. In the training objective function (below line 177) of GenGNN, an additional ELBO loss is added to the loss of GCN/GAT to regularize their parameters. According to authors’ explanation in lines 181-182, this additional loss enforces the learned GCN/GAT to support the graph (G) generation while conforming to the label (Y) generation (by an MLP) without the graph. There seems to be some contradiction/tradeoff here, and I find it hard to comprehend. Why would the regularization help to train a better GCN/GAT for the missing-edge setting? The authors should provide better explanation than simply saying it would improve generalization as in line 244. Perhaps an ablation study would help to understand the contribution of each regularization term in the objective function? Also, the setting of the missing-edge experiment seems too “extreme”. To mimic the scenario of new users in a network, shouldn’t it be more reasonable to randomly set aside a small portion of nodes (as new users) instead of 1000 nodes (about 1/3 of the nodes in Cora/CiteSeer) for testing? For the experiments on normal graphs, although the proposed method could improve GCN/GAT on Cora and CiteSeer, it also consistently decreases their performance on PubMed for both the standard and reduced-label settings (similar to Bayesian GCN). Are the results on PubMed also statistically significant? The reason given by the authors in the paper and in their feedback says it is because the graph of PubMed is denser than that of Cora and CiteSeer, which sounds reasonable but vague. Like the missing-edge experiment, it would be more interesting to provide some insights from the training objective function while taking into account graph properties. -2. Thanks for the comparison to Bayesian GCN. In my opinion, it is OK to follow the hyperparameters of GCN/GAT, but the proposed method should be able to perform well (train reasonable model parameters) without using the validation set to ensure its practical use for semi-supervised learning. For GCN/GAT, I know they used the validation set in the original papers, but they can do well without using the validation set for model selection given 20 labels per class on the citation networks (verified in the experiments of Bayesian GCN and other papers). With fewer labels such as 10 or 5 per class, there will be a significant performance gap between with and w/o the validation set. Bayesian GCN did not use the validation set for model selection, which makes their results more convincing. It would be informative to show how the proposed method would perform without using the validation set for model selection/early stopping, especially for the reduced-label setting and the missing-edge setting. Other comments: There is a vast literature on semi-supervised learning, and graph neural networks is a fast-developing field. I find the listed references are a bit insufficient. It would be informative to include more recent works on GNN for discussion or comparison. My final assessment：I think the proposed generative model is valid and may have potentials, but for a NeurIPS paper, I would expect a clearer interpretation of model behavior or a more complete empirical evaluation. It would be better if the authors could clearly explain the benefits of GenGNN, i.e., in what scenarios it could improve GCN/GAT and more importantly WHY. So far, the message conveyed in this paper is not so clear, and the experimental results are not very convincing. I think this work still needs much revision to make a real impact/solid contribution to the field. Therefore, I tend to keep my previous rating.