Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport
This work addresses data incompleteness in knowledge graphs for applications like information retrieval, with incremental improvements in query embedding techniques.
The paper tackles the problem of answering complex queries on incomplete knowledge graphs by proposing a new query embedding method that balances local comparison and global transport using unbalanced optimal transport theory, achieving performance improvements over existing methods on standard datasets, complex queries, and hierarchical knowledge graphs.
Answering complex queries on knowledge graphs is important but particularly challenging because of the data incompleteness. Query embedding methods address this issue by learning-based models and simulating logical reasoning with set operators. Previous works focus on specific forms of embeddings, but scoring functions between embeddings are underexplored. In contrast to existing scoring functions motivated by local comparison or global transport, this work investigates the local and global trade-off with unbalanced optimal transport theory. Specifically, we embed sets as bounded measures in $\real$ endowed with a scoring function motivated by the Wasserstein-Fisher-Rao metric. Such a design also facilitates closed-form set operators in the embedding space. Moreover, we introduce a convolution-based algorithm for linear time computation and a block-diagonal kernel to enforce the trade-off. Results show that WFRE can outperform existing query embedding methods on standard datasets, evaluation sets with combinatorially complex queries, and hierarchical knowledge graphs. Ablation study shows that finding a better local and global trade-off is essential for performance improvement.