Embedding Logical Queries on Knowledge Graphs (1806.01445v4)

Abstract: 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 "em what drugs are likely to target proteins involved with both diseases X and Y?" -- a query that requires reasoning about all possible proteins that {\em 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.

• The paper introduces a framework that embeds nodes and logical operators to efficiently handle complex conjunctive queries on incomplete knowledge graphs.
• It employs projection and intersection operators to translate logical queries into geometric operations, reducing computation to O(d²E) operations.
• Empirical evaluations on biological and social network datasets show a notable performance improvement, including an AUC of 91.0 on drug-gene-disease interactions.

Embedding Logical Queries on Knowledge Graphs: An Analysis

"Embedding Logical Queries on Knowledge Graphs" presents a framework designed to efficiently handle and predict conjunctive logical queries on incomplete knowledge graphs. This framework builds on the growing domain of knowledge graph embeddings, transitioning beyond mere simple edge prediction to tackling more complex logical operations that involve multiple unobserved edges and variables within a graph structure.

Core Contributions

The essence of the framework lies in its ability to embed graph nodes within a low-dimensional space, where logical operators are translated into learned geometric operations. Specifically, the paper introduces two primary operations: projection and intersection. These geometric operations allow the framework to answer queries in a dimensionally reduced space with linear time complexity relative to the number of query variables. This is a marked improvement over traditional approaches which require exponential time for graph enumeration.

Methodological Overview

The detailed methodology encompasses two prime components: the projection operator and the intersection operator:

1. Projection Operator (P): Handles edge prediction by translating onto new embeddings that represent unions of sets reachable according to specific relations.
2. Intersection Operator (I): Informed by deep learning advances in set operations, this operator computes intersections across sets brought forward by the query's structure.

Together, these components facilitate the reduction of query embedding generation to $O(d^2E)$ operations, where $d$ is the embedding dimension and $E$ is the number of query edges—achieving an efficient operation even in networks comprising millions of entries.

Empirical Evaluation

The practical utility of the framework is demonstrated through application studies on real-world datasets, notably, a biological interaction network concerning drug-gene-disease interoperability and social interaction networks derived from Reddit forum data. Performance metrics show a notable advantage over baseline methods. In the biological dataset, the proposed embeddings achieved an AUC of 91.0, indicating material improvement over models focused solely on edge predictions. Furthermore, the detailed breakdown of performance across varying query structures demonstrates its robustness and versatility.

Theoretical Implications

From a theoretical standpoint, the proposed model equates the task of handling conjunctive graph queries with a systematic sequence of geometric modifications within low-dimensional spaces—offering a mathematically grounded approach to query embedding. This not only enhances understanding but opens pathways for embedding more complex logical structures and computational theorems in knowledge graph contexts.

Future Directions

Pertaining to future research trajectories, the framework's extension to handle richer logical expressions, such as disjunctions and negations, would be a logical progression. Incorporating temporal or sequential data, which can amplify the predictive capacity in evolving networks, is another avenue for exploration.

Conclusion

This paper contributes substantially to the field of knowledge graph embeddings by addressing the complex interplay of logical queries and low-dimensional representations. The proposed approach not only augments the computational efficiency of traditional models but also enhances the adaptability and functionality of knowledge graph applications. As knowledge graphs continue to underpin diverse technological markets—from biomedical discovery to social media analytics—the implications of such innovations will likely propagate significant advances in knowledge inference and decision-making systems.