Utilizing Description Logics for Global Explanations of Heterogeneous Graph Neural Networks

Graph Neural Networks (GNNs) are effective for node classification in graph-structured data, but they lack explainability, especially at the global level. Current research mainly utilizes subgraphs of the input as local explanations or generates new graphs as global explanations. However, these graph-based methods are limited in their ability to explain classes with multiple sufficient explanations. To provide more expressive explanations, we propose utilizing class expressions (CEs) from the field of description logic (DL). Our approach explains heterogeneous graphs with different types of nodes using CEs in the EL description logic. To identify the best explanation among multiple candidate explanations, we employ and compare two different scoring functions: (1) For a given CE, we construct multiple graphs, have the GNN make a prediction for each graph, and aggregate the predicted scores. (2) We score the CE in terms of fidelity, i.e., we compare the predictions of the GNN to the predictions by the CE on a separate validation set. Instead of subgraph-based explanations, we offer CE-based explanations.

Causal Question Answering with Reinforcement Learning

Causal questions inquire about causal relationships between different events or phenomena. Specifically, they often aim to determine whether there is a relationship between two phenomena, or to identify all causes/effects of a phenomenon. Causal questions are important for a variety of use cases, including virtual assistants and search engines. However, many current approaches to causal question answering cannot provide explanations or evidence for their answers. Hence, in this paper, we aim to answer causal questions with CauseNet, a large-scale dataset of causal relations and their provenance data. Inspired by recent, successful applications of reinforcement learning to knowledge graph tasks, such as link prediction and fact-checking, we explore the application of reinforcement learning on CauseNet for causal question answering. We introduce an Actor-Critic based agent which learns to search through the graph to answer causal questions. We bootstrap the agent with a supervised learning procedure to deal with large action spaces and sparse rewards. Our evaluation shows that the agent successfully prunes the search space to answer binary causal questions by visiting less than 30 nodes per question compared to over 3,000 nodes by a naive breadth-first search. Our ablation study indicates that our supervised learning strategy provides a strong foundation upon which our reinforcement learning agent improves. The paths returned by our agent explain the mechanisms by which a cause produces an effect. Moreover, for each edge on a path, CauseNet stores its original source on the web allowing for easy verification of paths.

Universal Knowledge Graph Embeddings

A variety of knowledge graph embedding approaches have been developed. Most of them obtain embeddings by learning the structure of the knowledge graph within a link prediction setting. As a result, the embeddings reflect only the semantics of a single knowledge graph, and embeddings for different knowledge graphs are not aligned, e.g., they cannot be used to find similar entities across knowledge graphs via nearest neighbor search. However, knowledge graph embedding applications such as entity disambiguation require a more global representation, i.e., a representation that is valid across multiple sources. We propose to learn universal knowledge graph embeddings from large-scale interlinked knowledge sources. To this end, we fuse large knowledge graphs based on the owl:sameAs relation such that every entity is represented by a unique identity. We instantiate our idea by computing universal embeddings based on DBpedia and Wikidata yielding embeddings for about 180 million entities, 15 thousand relations, and 1.2 billion triples. Moreover, we develop a convenient API to provide embeddings as a service. Experiments on link prediction show that universal knowledge graph embeddings encode better semantics compared to embeddings computed on a single knowledge graph. For reproducibility purposes, we provide our source code and datasets open access at https://github.com/dice-group/Universal_Embeddings

LitCQD: Multi-Hop Reasoning in Incomplete Knowledge Graphs with Numeric Literals

Most real-world knowledge graphs, including Wikidata, DBpedia, and Yago are incomplete. Answering queries on such incomplete graphs is an important, but challenging problem. Recently, a number of approaches, including complex query decomposition (CQD), have been proposed to answer complex, multi-hop queries with conjunctions and disjunctions on such graphs. However, all state-of-the-art approaches only consider graphs consisting of entities and relations, neglecting literal values. In this paper, we propose LitCQD -- an approach to answer complex, multi-hop queries where both the query and the knowledge graph can contain numeric literal values: LitCQD can answer queries having numerical answers or having entity answers satisfying numerical constraints. For example, it allows to query (1)~persons living in New York having a certain age, and (2)~the average age of persons living in New York. We evaluate LitCQD on query types with and without literal values. To evaluate LitCQD, we generate complex, multi-hop queries and their expected answers on a version of the FB15k-237 dataset that was extended by literal values.

Counterfactual Explanations for Concepts in $\mathcal{ELH}$

Knowledge bases are widely used for information management on the web, enabling high-impact applications such as web search, question answering, and natural language processing. They also serve as the backbone for automatic decision systems, e.g. for medical diagnostics and credit scoring. As stakeholders affected by these decisions would like to understand their situation and verify fair decisions, a number of explanation approaches have been proposed using concepts in description logics. However, the learned concepts can become long and difficult to fathom for non-experts, even when verbalized. Moreover, long concepts do not immediately provide a clear path of action to change one's situation. Counterfactuals answering the question "How must feature values be changed to obtain a different classification?" have been proposed as short, human-friendly explanations for tabular data. In this paper, we transfer the notion of counterfactuals to description logics and propose the first algorithm for generating counterfactual explanations in the description logic $\mathcal{ELH}$. Counterfactual candidates are generated from concepts and the candidates with fewest feature changes are selected as counterfactuals. In case of multiple counterfactuals, we rank them according to the likeliness of their feature combinations. For evaluation, we conduct a user survey to investigate which of the generated counterfactual candidates are preferred for explanation by participants. In a second study, we explore possible use cases for counterfactual explanations.

Neural Class Expression Synthesis

Class expression learning is a branch of explainable supervised machine learning of increasing importance. Most existing approaches for class expression learning in description logics are search algorithms or hard-rule-based. In particular, approaches based on refinement operators suffer from scalability issues as they rely on heuristic functions to explore a large search space for each learning problem. We propose a new family of approaches, which we dub synthesis approaches. Instances of this family compute class expressions directly from the examples provided. Consequently, they are not subject to the runtime limitations of search-based approaches nor the lack of flexibility of hard-rule-based approaches. We study three instances of this novel family of approaches that use lightweight neural network architectures to synthesize class expressions from sets of positive examples. The results of their evaluation on four benchmark datasets suggest that they can effectively synthesize high-quality class expressions with respect to the input examples in under a second on average. Moreover, a comparison with the state-of-the-art approaches CELOE and ELTL suggests that we achieve significantly better F-measures on large ontologies. For reproducibility purposes, we provide our implementation as well as pre-trained models in the public GitHub repository at https://github.com/ConceptLengthLearner/NCES

EvoLearner: Learning Description Logics with Evolutionary Algorithms

Classifying nodes in knowledge graphs is an important task, e.g., predicting missing types of entities, predicting which molecules cause cancer, or predicting which drugs are promising treatment candidates. While black-box models often achieve high predictive performance, they are only post-hoc and locally explainable and do not allow the learned model to be easily enriched with domain knowledge. Towards this end, learning description logic concepts from positive and negative examples has been proposed. However, learning such concepts often takes a long time and state-of-the-art approaches provide limited support for literal data values, although they are crucial for many applications. In this paper, we propose EvoLearner - an evolutionary approach to learn ALCQ(D), which is the attributive language with complement (ALC) paired with qualified cardinality restrictions (Q) and data properties (D). We contribute a novel initialization method for the initial population: starting from positive examples (nodes in the knowledge graph), we perform biased random walks and translate them to description logic concepts. Moreover, we improve support for data properties by maximizing information gain when deciding where to split the data. We show that our approach significantly outperforms the state of the art on the benchmarking framework SML-Bench for structured machine learning. Our ablation study confirms that this is due to our novel initialization method and support for data properties.

Prediction of concept lengths for fast concept learning in description logics

Concept learning approaches based on refinement operators explore partially ordered solution spaces to compute concepts, which are used as binary classification models for individuals. However, the refinement trees spanned by these approaches can easily grow to millions of nodes for complex learning problems. This leads to refinement-based approaches often failing to detect optimal concepts efficiently. In this paper, we propose a supervised machine learning approach for learning concept lengths, which allows predicting the length of the target concept and therefore facilitates the reduction of the search space during concept learning. To achieve this goal, we compare four neural architectures and evaluate them on four benchmark knowledge graphs--Carcinogenesis, Mutagenesis, Semantic Bible, Family Benchmark. Our evaluation results suggest that recurrent neural network architectures perform best at concept length prediction with an F-measure of up to 92%. We show that integrating our concept length predictor into the CELOE (Class Expression Learner for Ontology Engineering) algorithm improves CELOE's runtime by a factor of up to 13.4 without any significant changes to the quality of the results it generates. For reproducibility, we provide our implementation in the public GitHub repository at https://github.com/ConceptLengthLearner/ReproducibilityRepo

Convolutional Hypercomplex Embeddings for Link Prediction

Knowledge graph embedding research has mainly focused on the two smallest normed division algebras, $\mathbb{R}$ and $\mathbb{C}$. Recent results suggest that trilinear products of quaternion-valued embeddings can be a more effective means to tackle link prediction. In addition, models based on convolutions on real-valued embeddings often yield state-of-the-art results for link prediction. In this paper, we investigate a composition of convolution operations with hypercomplex multiplications. We propose the four approaches QMult, OMult, ConvQ and ConvO to tackle the link prediction problem. QMult and OMult can be considered as quaternion and octonion extensions of previous state-of-the-art approaches, including DistMult and ComplEx. ConvQ and ConvO build upon QMult and OMult by including convolution operations in a way inspired by the residual learning framework. We evaluated our approaches on seven link prediction datasets including WN18RR, FB15K-237 and YAGO3-10. Experimental results suggest that the benefits of learning hypercomplex-valued vector representations become more apparent as the size and complexity of the knowledge graph grows. ConvO outperforms state-of-the-art approaches on FB15K-237 in MRR, Hit@1 and Hit@3, while QMult, OMult, ConvQ and ConvO outperform state-of-the-approaches on YAGO3-10 in all metrics. Results also suggest that link prediction performances can be further improved via prediction averaging. To foster reproducible research, we provide an open-source implementation of approaches, including training and evaluation scripts as well as pretrained models.