Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However,
an open challenge in this area is developing techniques that can go beyond simple
edge prediction and handle more complex logical queries, which might involve
multiple unobserved edges, entities, and variables. For instance, given an incomplete biological knowledge graph, we might want to predict what drugs are likely
to target proteins involved with both diseases X and Y?—a query that requires
reasoning about all possible proteins that might interact with diseases X and Y.
Here we introduce a framework to efficiently make predictions about conjunctive
logical queries—a flexible but tractable subset of first-order logic—on incomplete
knowledge graphs. In our approach, we embed graph nodes in a low-dimensional
space and represent logical operators as learned geometric operations (e.g., translation, rotation) in this embedding space. By performing logical operations within a
low-dimensional embedding space, our approach achieves a time complexity that
is linear in the number of query variables, compared to the exponential complexity
required by a naive enumeration-based approach. We demonstrate the utility of
this framework in two application studies on real-world datasets with millions
of relations: predicting logical relationships in a network of drug-gene-disease
interactions and in a graph-based representation of social interactions derived from
a popular web forum.
