Neural-based Mixture Probabilistic Query Embedding for Answering FOL queries on Knowledge Graphs

Query embedding (QE)—which aims to embed entities and first-order logical (FOL) queries in a vector space, has shown great power in answering FOL queries on knowledge graphs (KGs). Existing QE methods divide a complex query into a sequence of mini-queries according to its computation graph and perform logical operations on the answer sets of mini-queries to get answers. However, most of them assume that answer sets satisfy an individual distribution (e.g., Uniform, Beta, or Gaussian), which is often violated in real applications and limit their performance. In this paper, we propose a Neural-based Mixture Probabilistic Query Embedding Model (NMP-QEM) that encodes the answer set of each mini-query as a mixed Gaussian distribution with multiple means and covariance parameters, which can approximate any random distribution arbitrarily well in real KGs. Additionally, to overcome the difficulty in defining the closed solution of negation operation, we introduce neural-based logical operators of projection, intersection and negation for a mixed Gaussian distribution to answer all the FOL queries. Extensive experiments demonstrate that NMP-QEM significantly outperforms existing state-of-the-art methods on benchmark datasets. In NELL995, NMP-QEM achieves a 31% relative improvement over the state-of-the-art.