DEEP GAUSSIAN EMBEDDING OF GRAPHS: UNSUPERVISED INDUCTIVE LEARNING VIA RANKING
Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss -an approach that can efficiently learn versatile node embeddings on large scale (attributed) graphs that show strong performance on tasks such as link prediction and node classification. Unlike most approaches that represent nodes as point vectors in a low-dimensional continuous space, we embed each node as a Gaussian distribution, allowing us to capture uncertainty about the representation. Furthermore, we propose an unsupervised method that handles inductive learning scenarios and is applicable to different types of graphs: plain/attributed, directed/undirected. By leveraging both the network structure and the associated node attributes, we are able to generalize to unseen nodes without additional training. To learn the embeddings we adopt a personalized ranking formulation w.r.t. the node distances that exploits the natural ordering of the nodes imposed by the network structure. Experiments on real world networks demonstrate the high performance of our approach, outperforming state-of-the-art network embedding methods on several different tasks. Additionally, we demonstrate the benefits of modeling uncertainty -by analyzing it we can estimate neighborhood diversity and detect the intrinsic latent dimensionality of a graph.
This paper proposes Graph2Gauss (G2G), a node embedding method that embeds nodes in attributed graphs (can work w/o attributes as well) into Gaussian distributions rather than conventionally latent vectors. By doing so, G2G can reflect the uncertainty of a node's embedding. The authors then use these Gaussian distributions and neighborhood ranking constraints to obtain the final node embeddings. Experiments on link prediction and node classification showed improved performance over several strong embedding methods. Overall, the paper is well-written and the contributions are remarkable. The reason I am giving a less possible rating is that some statements are questionable and can severely affect the conclusions claimed in this paper, which therefore requires the authors' detailed response. I am certainly willing to change my rating if the authors clarify my questions.
Major concern 1: Is the latent vector dimension L really the same for G2G and other compared methods? 
In the first paragraph of Section 4, it is stated that "in all experiments if the competing techniques use an embedding of
dimensionality L, G2G’s embedding is actually only half of this dimensionality so that the overall number of ’parameters’ per node (mean vector + variance terms) matches L."  This setting can be wrong since the degree of freedom of a L-dim Gaussian distribution should be L+L(L-1)/2, where the first term corresponds to the mean and the second term corresponds to the covariance. If I understand it correctly, when any compared embedding method used an L-dim vector, the authors used the dimension of L/2. But this setting is wrong if one wants the overall number of ’parameters’ per node (mean vector + variance terms) matches L, as stated by the authors. Fixing L, the equivalent dimension L_G2G for G2G should be set such that L_G2G +L_G2G (L_G2G -1)/2=L, not 2*L_G2G=L.  Since this setting is universal to the follow-up analysis and may severely degrade the performance of GSG due to less embedding dimensions, I hope the authors can clarify this point.
Major concern 2: The claim on inductive learning
Inductive learning is one of the major contributions claimed in this paper. The authors claim G2G can learn an embedding of an unseen node solely based on their attributes. However, is it not clear why this can be done. In the learning stage of Sec. 3.3, the attributes do not seem to play a role in the energy function. Also, since no algorithm descriptions are available, it's not clear how using only an unseen node's attributes can yield a good embedding under G2G work (so does Sec. 4.5). 
Moreover, how does it compare to directly using raw user attributes for these tasks?
Minor concern/suggestions: The "similarity" measure in section 3.1 using KL divergence should be better rephased by "dissimilarity" measure. Otherwise, one has a similarity measure $Delta$ and wants it to increase as the hop distance k decreases (closer nodes are more similar). But the ranking constraints are somewhat counter-intuitive because you want $Delta$ to be small if nodes are closer. There is nothing wrong with the ranking condition, but rather an inconsistency between the use of "similarity" measure for KL divergence.