Abstract

Over the last decade, there has been an increasing interest in relational machine learning (RML), which studies methods for the statistical analysis of relational or graph-structured data. Relational data arise naturally in many real-world applications, including social networks, recommender systems, and computational finance. Such data can be represented in the form of a graph consisting of nodes (entities) and labeled edges (relationships between entities). While traditional machine learning techniques are based on feature vectors, RML takes relations into account and permits inference among entities. Recently, performing prediction and learning tasks on knowledge graphs has become a main topic in RML. Knowledge graphs (KGs) are widely used resources for studying multi-relational data in the form of a directed graph, where each labeled edge describes a factual statement, such as (Munich, locatedIn, Germany). Traditionally, knowledge graphs are considered to represent stationary relationships, which do not change over time. In contrast, event-based multi-relational data exhibits complex temporal dynamics in addition to its multi-relational nature. For example, the political relationship between two countries would intensify because of trade fights; the president of a country may change after an election. To represent the temporal aspect, temporal knowledge graphs (tKGs) were introduced that store a temporal event as a quadruple by extending the static triple with a timestamp describing when this event occurred, i.e. (Barack Obama, visit, India, 2010-11-06). Thus, each edge in the graph has temporal information associated with it and may recur or evolve over time. Among various learning paradigms on KGs, knowledge representation learning (KRL), also known as knowledge graph embedding, has achieved great success. KRL maps entities and relations into low-dimensional vector spaces while capturing semantic meanings. However, KRL approaches have mostly been done for static KGs and lack the ability to utilize rich temporal dynamics available on tKGs. In this thesis, we study state-of-the-art representation learning techniques for temporal knowledge graphs that can capture temporal dependencies across entities in addition to their relational dependencies. We discover representations for two inference tasks, i.e., tKG forecasting and completion. The former is to forecast future events using historical observations up to the present time, while the latter predicts missing links at observed timestamps. For tKG forecasting, we show how to make the reasoning process interpretable while maintaining performance by employing a sequential reasoning process over local subgraphs. Besides, we propose a continuous-depth multi-relational graph neural network with a novel graph neural ordinary differential equation. It allows for learning continuous-time representations of tKGs, especially in cases with observations in irregular time intervals, as encountered in online analysis. For tKG completion, we systematically review multiple benchmark models. We thoroughly investigate the significance of the proposed temporal encoding technique in each model and provide the first unified open-source framework, which gathers the implementations of well-known tKG completion models. Finally, we discuss the power of geometric learning and show that learning evolving entity representations in a product of Riemannian manifolds can better reflect geometric structures on tKGs and achieve better performances than Euclidean embeddings while requiring significantly fewer model parameters.