Probabilistic Entity Representation Model for Reasoning over Knowledge Graphs

TL;DR

This paper introduces PERM, a probabilistic model using Gaussian embeddings for logical reasoning over Knowledge Graphs, improving accuracy and interpretability over existing geometric methods.

Contribution

The paper proposes a novel Gaussian-based entity representation model that enables smooth, closed logical operations for reasoning over Knowledge Graphs, surpassing prior geometric approaches.

Findings

PERM outperforms state-of-the-art methods on benchmark datasets.

PERM achieves better drug-repurposing F1 scores in COVID-19 case study.

Gaussian embeddings provide interpretable visualizations of reasoning processes.

Abstract

Logical reasoning over Knowledge Graphs (KGs) is a fundamental technique that can provide efficient querying mechanism over large and incomplete databases. Current approaches employ spatial geometries such as boxes to learn query representations that encompass the answer entities and model the logical operations of projection and intersection. However, their geometry is restrictive and leads to non-smooth strict boundaries, which further results in ambiguous answer entities. Furthermore, previous works propose transformation tricks to handle unions which results in non-closure and, thus, cannot be chained in a stream. In this paper, we propose a Probabilistic Entity Representation Model (PERM) to encode entities as a Multivariate Gaussian density with mean and covariance parameters to capture its semantic position and smooth decision boundary, respectively. Additionally, we also define the closed logical operations of projection, intersection, and union that can be aggregated using an end-to-end objective function. On the logical query reasoning problem, we demonstrate that the proposed PERM significantly outperforms the state-of-the-art methods on various public benchmark KG datasets on standard evaluation metrics. We also evaluate PERM's competence on a COVID-19 drug-repurposing case study and show that our proposed work is able to recommend drugs with substantially better F1 than current methods. Finally, we demonstrate the working of our PERM's query answering process through a low-dimensional visualization of the Gaussian representations.