Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: This paper studies the problem of graph generation, and proposes a new model using both micro and macro level supervision information in GraphVAE architecture. Fitting adjacency matrix is the micro supervision, and three kinds of graph statistics, i.e., degree histogram, number of triangles, and higher-order proximity relations, are adopted as macro supervision. The object consists of ELBOs modeling micro-macro loss and a KL-divergence between the prior and the approximate posterior of hidden representation.  The proposed model is validated on 3 synthetic, and 2 real-world graph datasets. The experimental results the proposed model generates graphs with a lower discrepancy between generated and test graph embeddings than graphs generated by competitors in terms of MMD RBF and F1 PR.
strengths_and_weaknesses: Strong points:

S1. The macro objective of fitting graph statistics in graph generation is novel to me. 

S2. The paper proposes a general micro-macro ELBO as the objective, and then implements the ELBO by graph neural networks.

S3. The experimental results show the proposed model outperforms the competitors.

Weak points:

W1. It is not clear how the graph generation task benefits from fitting graph statistics. In other words, what is the limitation to only fitting adjacency matrix in graph generation? From this line, I have a concern about what kind of graph statistics should be chosen as targets？
This paper selects three graph statistics, but does not present an explanation for this selection. 

W2. The efficiency. Both calculating and fitting graph statistics bring new computing costs, e.g., the complexity is $O(n^3)$ to compute the transition probability matrix.

W3. It is not clear how to form descriptor functions with respect to vector label histogram and triangle count. And how to guarantee the descriptor functions are differentiable.
questions: Q1.  How the graph generation task benefits from fitting graph statistics. And what kind of graph statistics should be chosen as targets？

Q2. How to form descriptor functions with respect to vector label histogram and triangle count?
limitations: Yes.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The contributions of this paper was to model graph data jointly at two levels: a micro level based on local
information and a macro level based on aggregate graph statistics.
strengths_and_weaknesses: Positives:

1. The idea of this work is interesting and novel, which trys to use probabilistic model to explore the local and global graph statistics.

2. The performance of this work is very good, comparing to the existing GraphVAE. And the code is available.

Negathive:
1. The scalability of this work may be a challenge, the compexity of the descriptors is either O(N^2) or  O(N^3). Also the algorithm reuqires pre-define a graph descriptors to compute the graph statistics.

2. The algorithm part is straightforwad. Basically, it designs a MM loss into one unified fraemwork. It seems that many GAN-based models can achieve the similar function. Any discussion?

questions: 1. How the proposed model is different from the GAN-based model? 
limitations: Yes
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper jointly models micro and macro level graph information for graph generation. A principled joint probabilistic model for both levels is proposed and an ELBO training objective is derived for graph encoder-decoder models. Extensive experiments and visualization results validate the efficacy of adding micro-macro modelling to GraphVAE models for graph generation.
strengths_and_weaknesses: Strengths:
1. This paper is well motivated and the idea of utilizing node-level properties and graph-level statistics to constrain graph generation seems reasonable.
2. The design of micro-macro (MM) loss is clear and theoretically solid.
3. The authors have done a thorough analysis of the proposed model and validated its effectiveness through qualitative and quantitative evaluation. The main claims are supported by the experimental results.

Weaknesses:
My main concern is that the proposed objective function is only applied on GraphVAE following an AB design. Although the experimental results are satisfactory on graph generation, it remains unclear whether the benefits of micro-macro modeling would generalise to other models. 

questions: The proposed MM objective function is applied on GraphVAE for an AB design and its effectiveness is showed for graph generation. Do you think if the benefits of micro-macro modeling would generalise to other models or other graph tasks? Some related discussions in this regard are necessary.
limitations: The authors have adequately discussed the limitations of their work.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The authors of this paper newly presented a function that can reflect graph statistics in the graph generative model. They have shown various experiments and visualizations proving graph statistics are well-reflected. In addition, designing an objective function to reflect different graph statistics simply is a significant contribution.
strengths_and_weaknesses: Originality: (Yes) 
The proposed method seems to be original in that the authors proposed a new but simple VAE-based objective function to reflect graph statistics.

Quality: (Neutral) 
Since the purpose of this study is to generate graphs that reflect graph statistics, theoretical support and experiments for the purpose are well shown. However, the performance on real-world datasets such as the molecule is marginal. In particular, when only one graph statistic is used, the performance degradation is greater than that of GraphVAE, which needs clarification. Since it shows good performance only when all three statistics presented in the paper are written, it is necessary to explain why these three combinations were selected and what synergy they show.

Clarity: (Yes) 
There was no difficulty in understanding what the paper was trying to say, and it shows sufficient proof of the formula. I think it would be easier to understand if the architecture overview was attached. I suggest adding a picture of the structure for the reader's clear understanding.

Significance: (Neutral) 
This model seems to have particular strengths in experiments using Synthetic datasets. In addition, it seems to be a good contribution that it showed a higher performance improvement compared to GraphVAE. However, as discussed in the paper, performance in real-world datasets seems to be more important to contribute in practical areas such as molecule and medical discovery. However, the experimental results presented in the paper do not support this.  Additional experiments will be needed to show that graphs are well generated using the QM9 dataset shown in GraphVAE.


questions: 1. As a result of examining the paper or code, it seems that node feature or edge feature is not generated. In the case of using the Real-world dataset, it is considered important to generate not only the structure of the graph but also the node/edge feature well. Can you suggest an experiment related to this part?  

2. As described in the paper, graph statistics are reflected using the calibrated Gaussian framework. There are two questions about this.  
        a) Are graph statistics used for performance evaluation or reflected in objective function actually following Gaussian distribution? For example, if you think about 'degrees', it seems that the skew distribution is easy to appear due to the nature of the graph dataset. If so, it seems necessary to verify whether 'degrees' can be assumed to follow Gaussian distribution.  
        b) Can graph statistics be reflected in other ways without utilizing the calibrated Gaussian framework? Is there an experiment that can support the evidence using the Calibrated Gaussian framework?        

3. Figure 1 shows 'connected components' as an example to be improved in this paper. It would be nice to show that the proposed model has improved this part well.

limitations: The positive social impacts presented in this paper include molecular presentation and medical discovery. However, since the model proposed by real-world dataset shows weak performance, it is seen as an important limitation.
review_title: null

Meta-review: metareview: This paper proposes a new generative model for the generation of graphs. Different from most of existing approaches, the proposed method considers both node and graph level properties to capture high-order connectivity and overcome sparsity of any observed graph. The writing is general clear and the results are convincing. The reviewers are overall positive, with some concerns on the motivation, which has been addressed well by the authors in the rebuttal. Some other questions raised by the reviewers are also appropriately addressed, which leads to the increase of some scores. The downside of the approach lies in the time complexity in collecting the macro-level statistics. But overall, it is a good paper worth accepting.
confidence: Certain
Decision: Accept