  Many practical graph problems, such as knowledge graph construction and
drug-drug interaction prediction, require to handle multi-relational graphs.
However, handling real-world multi-relational graphs with Graph Neural Networks
(GNNs) is often challenging due to their evolving nature, as new entities
(nodes) can emerge over time. Moreover, newly emerged entities often have few
links, which makes the learning even more difficult. Motivated by this
challenge, we introduce a realistic problem of few-shot out-of-graph link
prediction, where we not only predict the links between the seen and unseen
nodes as in a conventional out-of-knowledge link prediction task but also
between the unseen nodes, with only few edges per node. We tackle this problem
with a novel transductive meta-learning framework which we refer to as Graph
Extrapolation Networks (GEN). GEN meta-learns both the node embedding network
for inductive inference (seen-to-unseen) and the link prediction network for
transductive inference (unseen-to-unseen). For transductive link prediction, we
further propose a stochastic embedding layer to model uncertainty in the link
prediction between unseen entities. We validate our model on multiple benchmark
datasets for knowledge graph completion and drug-drug interaction prediction.
The results show that our model significantly outperforms relevant baselines
for out-of-graph link prediction tasks.
