We consider the task of few shot link prediction, where the goal is to predict missing edges across multiple graphs using only a small sample of known edges. We show that current link prediction methods are generally ill-equipped to handle this task-as they cannot effectively transfer knowledge between graphs in a multigraph setting and are unable to effectively learn from very sparse data. To address this challenge, we introduce a new gradient-based meta learning framework, Meta-Graph, that leverages higher-order gradients along with a learned graph signature function that conditionally generates a graph neural network initialization. Using a novel set of few shot link prediction benchmarks, we show that MetaGraph enables not only fast adaptation but also better final convergence and can effectively learn using only a small sample of true edges.
Overview: In this paper, a meta-learning approach is proposed to perform link prediction across multi-graphs with scarce data. To do so, each graph is treated as a link prediction "task". Different from the tasks in conventional meta-learning, the graphs here are generally non i.i.d. Based on the variational graph auto-coders, the method learns two important components: the global parameters used for GNNs and a graph signature function used to modulate the parameters of inference model based on the history of observed training graphs. 
The idea of formulating link prediction as a few-shot learning problem and solving it via multi-graph meta-learning is novel. The approach basically takes advantage of meta-learning and is expected to generalize well across graphs. The numerical study is extensive in discussing the properties of meta-graph and showing more attractive empirical performance than the existing approaches. 
Comments:
1. The explanation of Figure 1 needs to be improved. In its current form, the figure does not illustrate the idea of this paper very clearly. It would be better to provide more explanations on the graphical model for meta-graph and the meta-graph architecture in the context. 
2. The description of Algorithm 1 is confusing in some places. For example, the operation in Line 6 is commented as *compute graph signature*. However, what's actually going on is to set the signature function to stop gradient computation which seems not matching the comment. 
3. In section 4.2, the 5-gradient update AUC is reported to show the fast adaptation of meta-graph. However, in my opinion, it could be much more informative to show the accuracies of different gradient steps, like what has done in the experimental study of MAML. I don’t think the current experimental results can well explain the property of fast adaptation. 
=== update after author response ===
Thank you for your response.   I find my main concerns properly addressed in the feedback.