Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 3: Weak Reject
review_content: The paper proposes an extension of learning graph structure and GNN concurrently, by considering that real-world graphs are often noisy and incomplete. The idea of optimizing the intrinsic graph structure iteratively for down-stream prediction tasks is interesting. Experimental results demonstrate the effectiveness of proposed method. 

Strengths:
1）the paper proposes a learnable similarity metric function and a graph regularization for learning an optimal graph structure for prediction.
2）Besides raw node features, the paper attempts to optimize graph structures via learned node embeddings in an iterative manner. 
3）The paper is easy to read, and experiments show that the proposed method performs well.

Weaknesses:
1）Compared with LDS [1], this work seems to overlook the bi-level optimization problem for learning model parameters based on the optimal graph structure. The reason behind this method is expected. 
2）Although the paper claims that the dependence of raw node features for learning graph structure has been weakened,  empirical analysis on this point is not given. The feature matrices in experiments are not strictly independent with graph structures.
3) As shown in Appendix B, too many hyper-parameters are involved. I conjecture it will be difficult to reproduce the experimental results.
4) Eqs.(2), (3) and (10) are problematic. Node embeddings Z should be included in them. Eq.(10) does not have theoretical proof. According to Eq.(10), the method cannot handle graphs with noisy edges. In experiments, there are edge deletions, but no edge addings. Experiments with attacked graph are expected.
5) Although this method is claimed efficient, it is indeed slower than the classic GNNs due to the iterative operation. The details of training time comparison between this method and GNNs such as GCN and GAT will be helpful. I was wondering why this method is faster than LDS. Is it due to removing the bi-level optimization problem ? 
6) Although the method can handle inductive training, it is hardly scale to big networks. Pubmed is an open citation network with around 20,000 nodes similar to Cora and Citeseer. Those three datasets are popularly used in GNNs as testbed. However, Pubmed is not used in this work. I conjecture that the new method cannot handle such a big dataset efficiently.

Overall, this proposed method is well motivated, but the technical novelty is limited. 

review_title: Official Blind Review #2

final_score: rating: 6: Weak Accept
review_content: The paper introduces an iterative method called IDGL for learning both the graph structure (more precisely adjacency matrix) and parameters of the graph neural network.

The idea of iteratively refining an adjacency matrix A to obtain sparsity and smoothness is interesting and the experimental results are quite supportive. The main issue here is that the regularization terms in Eqs. 4, 5, 6 (which should be considered to be the most important in the paper) are exactly similar to those in [1] (see Eq. 12 in [1]).  This reduces the novelty of the paper.

Other parts in the paper such as using similarity between nodes (e.g. self-attention) to compute adjacency matrix or using the learned adjacency matrix with graph neural network is not new and have been done by many other works. There is also the rich related literature on graph generation (e.g., as in drug design), graph transformation (e.g., as in chemical reaction), structure learning in classical probabilistic graphical models, graph pooling (which is essentially building new latent graphs from an original graph), knowledge-graph completion, etc. This is not to say that the problem is solved (it isn't), but it is fair to place this work in a broader context.

About the experiments, I have several concerns. First, I am not sure why the authors say that LDS [2] does not support inductive learning? LDS uses input node features to learn the unknown graph structure so I think it should be able to do inductive learning. DeepWalk or Node2Vec are examples of transductive methods because they do not use the node features. Second, for the running time comparison between IDGL and LDS, what are the size and number of parameters used in each model since they greatly affect the running time.

Minor point: please clean up duplicates in the reference list.

[1] How to learn a graph from smooth signals, Kalofolias et. al. 2016
[2] Learning discrete structures for graph neural networks, Franceschi et. al. 2019.


review_title: Official Blind Review #1

final_score: rating: 3: Weak Reject
review_content: This paper leverages metric learning to learn graph structure jointly with the learning of graph embedding. Firstly, it defines the similarity between any pair of nodes as the cosine similarity of nodal representations learned from attributes from nodes. Some tricks such as multi-head and sparsification are applied to learned cosine similarity to enhance the performance. Secondly, the authors introduce several graph regularizations to make the learned graph smooth, connected, sparse and non-trivial. Finally, the learned graph is linearly combined with the existing graph, using a hyperparameter \lambda. The convergence and time complexity are analyzed. The authors design experiments on five datasets. The paper also contains some issues:

1. Actually, the proposed framework is learning an extra graph adjacency matrix from nodal features, and further train GNN jointly on those two graphs. Therefore, the analysis of \lambda is necessary. However, this part is missing in the paper.

2. The improvements comparing with LDS is not significant. Besides, LDS only uses the optimized graph structure to train GNN, while the proposed framework use both learning structure and the original one (or the kNN result). It raises the question if the proposed framework can still out-perform LDS if LDS also takes the original graph as input to train GNN.

3. The learned graph should be better interpreted. For example, the cosine similarity on citation graphs with sparse features is very likely to be zero. As a result, the learned graph can be extremely sparse with very few non-zero entries. It would be interesting.

review_title: Official Blind Review #3

Meta-review: The submission proposes a method for learning a graph structure and node embeddings through an iterative process. Smoothness and sparsity are both optimized in this approach. The iterative method has a stopping mechanism based on distance from a ground truth. 

The concerns of the reviewers were about scalability and novelty. Since other methods have used the same costs for optimization, as well as other aspects of this approach, there is little contribution other than the iterative process. The improvement over LDS, the most similar approach, is relatively minor. 

Although the paper is promising, more work is required to establish the contributions of the method. Recommendation is for rejection.

Decision: Reject