Paper:
We propose an inductive matrix completion model without using side information. By factorizing the (rating) matrix into the product of low-dimensional latent embeddings of rows (users) and columns (items), a majority of existing matrix completion methods are transductive, since the learned embeddings cannot generalize to unseen rows/columns or to new matrices. To make matrix completion inductive, most previous works use content (side information), such as user's age or movie's genre, to make predictions. However, high-quality content is not always available, and can be hard to extract. Under the extreme setting where not any side information is available other than the matrix to complete, can we still learn an inductive matrix completion model? In this paper, we propose an Inductive Graphbased Matrix Completion (IGMC) model to address this problem. IGMC trains a graph neural network (GNN) based purely on local subgraphs around (user, item) pairs generated from the rating matrix and maps these subgraphs to their corresponding ratings. It achieves highly competitive performance with state-of-the-art transductive baselines. In addition, since IGMC is inductive, it can generalize to users/items unseen during the training (given that their ratings exist), and can even transfer to new tasks. Our transfer learning experiments show that a model trained out of the MovieLens dataset can be directly used to predict Douban movie ratings and works surprisingly well. Our work demonstrates that: 1) it is possible to train inductive matrix completion models without using side information while achieving similar or better performances than state-of-the-art transductive methods; 2) local graph patterns around a (user, item) pair are effective predictors of the rating this user gives to the item; and 3) Long-range dependencies might not be necessary for modeling recommender systems.

Review:
This paper presents a method for inductive matrix completion that does not rely on side information to make predictions. The approach is as follows: select the sub-graph from an h-hop neighbourhood of any target user-item pair (u,v) and relabel it according to its distance from (u, v). The authors then treat rating prediction as graph classification problem given the selected subgraph and use a graph convolution architecture to make the prediction. They achieve strong empirical performance in both the transductive and inductive settings. 
The paper presents an interesting approach to the inductive learning problem, with a number of interesting ideas and impressive empirical results. However, I have voted to reject this paper because I found the experimental section did a poor job of showing how the various ideas contribute to overall performance which made it difficult to evaluate the method beyond the absolute performance on benchmark datasets. 
The key idea of the paper is interesting - samples h-hop enclosing subgraphs and label the resulting nodes by their hop-length and type (i.e. users at hop length h get a different label to items at length h).  In their experiments they find that a model with only a 1-hop neighbourhood to performs so well, which suggests that for recommender systems, supporting long chains of dependencies is unnecessary. This is a useful property of the data that the method depends on, because without it, h-hop neighbourhoods with larger h would quickly include the whole graph on most datasets (most real-world graphs have small diameter).
They process these subgraphs with relational graph convolutions, but make two modifications: first they build their final representations by concatenating all the message passing steps (eq. 2) and both user and item representations (eq. 3), and second they have adjacent rating regularization which constrains weights between adjacent ratings. Eq.2 in particular is unusual because it  amounts to a skip connection from every layer (somewhat analogous to a DenseNet [Huang et al. 2015]). The authors say both lead to improved performance - but don’t evaluate the approaches in the experimental section. What is the contribution of eq 2, 3 and 6 relative to more standard approaches (i.e. no skip connections, sum pooling, no regularization)?
Finally - I found the positioning of the work of the work misleading: from the abstract and related worked we're told that this is a "seemingly impossible problem" and prior work has relied on side information to deal with the inductive case. From this description, we might infer that this is the first approach that deals with the no-side information case. But the clear baseline is Hartford et al. 2018 which also doesn't use side information for inductive matrix completion; and yet it is not mentioned in either the introduction or the related work sections. This omission is unfortunate because both because it's misleading, and more importantly it misses the opportunity to discuss the relative merits of the approaches (beyond performance, where this paper provides a clear improvement). For example,
 - How do the two methods compare with respect to computational complexity? This approach seems more expensive because a different subgraph is selected for each prediction (i.e. 1 forward pass per test set point rather than a single forward pass to compute the full test set), but this isn't discussed. 
 - Can you give any intuition about where the differences in performance are coming from?
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Increased rating to Weak Accept following the rebuttal below.