Query2GMM: Learning Representation with Gaussian Mixture Model for Reasoning over Knowledge Graphs

Logical query answering over Knowledge Graphs (KGs) is a fundamental yet complex task. A promising approach to achieve this is to embed queries and entities jointly into the same embedding space. Research along this line suggests that using multi-modal distribution to represent answer entities is more suitable than uni-modal distribution, as a single query may contain multiple disjoint answer subsets due to the compositional nature of multi-hop queries and the varying latent semantics of relations. However, existing methods based on multi-modal distribution roughly represent each subset without capturing its accurate cardinality, or even degenerate into uni-modal distribution learning during the reasoning process due to the lack of an effective similarity measure. To better model queries with diversified answers, we propose Query2GMM for answering logical queries over knowledge graphs. In Query2GMM, we present the GMM embedding to represent each query using a univariate Gaussian Mixture Model (GMM). Each subset of a query is encoded by its cardinality, semantic center and dispersion degree, allowing for precise representation of multiple subsets. Then we design specific neural networks for each operator to handle the inherent complexity that comes with multi-modal distribution while alleviating the cascading errors. Last, we define a new similarity measure to assess the relationships between an entity and a query's multi-answer subsets, enabling effective multi-modal distribution learning for reasoning. Comprehensive experimental results show that Query2GMM outperforms the best competitor by an absolute average of $5.5\%$. The source code is available at \url{https://anonymous.4open.science/r/Query2GMM-C42F}

Gravity-Inspired Graph Autoencoders for Directed Link Prediction

Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged as powerful node embedding methods. In particular, graph AE and VAE were successfully leveraged to tackle the challenging link prediction problem, aiming at figuring out whether some pairs of nodes from a graph are connected by unobserved edges. However, these models focus on undirected graphs and therefore ignore the potential direction of the link, which is limiting for numerous real-life applications. In this paper, we extend the graph AE and VAE frameworks to address link prediction in directed graphs. We present a new gravity-inspired decoder scheme that can effectively reconstruct directed graphs from a node embedding. We empirically evaluate our method on three different directed link prediction tasks, for which standard graph AE and VAE perform poorly. We achieve competitive results on three real-world graphs, outperforming several popular baselines.Comment: ACM International Conference on Information and Knowledge Management (CIKM 2019

New Embedded Representations and Evaluation Protocols for Inferring Transitive Relations

Beyond word embeddings, continuous representations of knowledge graph (KG) components, such as entities, types and relations, are widely used for entity mention disambiguation, relation inference and deep question answering. Great strides have been made in modeling general, asymmetric or antisymmetric KG relations using Gaussian, holographic, and complex embeddings. None of these directly enforce transitivity inherent in the is-instance-of and is-subtype-of relations. A recent proposal, called order embedding (OE), demands that the vector representing a subtype elementwise dominates the vector representing a supertype. However, the manner in which such constraints are asserted and evaluated have some limitations. In this short research note, we make three contributions specific to representing and inferring transitive relations. First, we propose and justify a significant improvement to the OE loss objective. Second, we propose a new representation of types as hyper-rectangular regions, that generalize and improve on OE. Third, we show that some current protocols to evaluate transitive relation inference can be misleading, and offer a sound alternative. Rather than use black-box deep learning modules off-the-shelf, we develop our training networks using elementary geometric considerations.Comment: Accepted at SIGIR 201