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Authors:Jiaoyan Chen, Olga Mashkova, Fernando Zhapa-Camacho, Robert Hoehndorf, Yuan He, Ian Horrocks

Abstract:Ontologies are widely used for representing domain knowledge and meta data, playing an increasingly important role in Information Systems, the Semantic Web, Bioinformatics and many other domains. However, logical reasoning that ontologies can directly support are quite limited in learning, approximation and prediction. One straightforward solution is to integrate statistical analysis and machine learning. To this end, automatically learning vector representation for knowledge of an ontology i.e., ontology embedding has been widely investigated in recent years. Numerous papers have been published on ontology embedding, but a lack of systematic reviews hinders researchers from gaining a comprehensive understanding of this field. To bridge this gap, we write this survey paper, which first introduces different kinds of semantics of ontologies, and formally defines ontology embedding from the perspectives of both mathematics and machine learning, as well as its property of faithfulness. Based on this, it systematically categorises and analyses a relatively complete set of over 80 papers, according to the ontologies and semantics that they aim at, and their technical solutions including geometric modeling, sequence modeling and graph propagation. This survey also introduces the applications of ontology embedding in ontology engineering, machine learning augmentation and life sciences, presents a new library mOWL, and discusses the challenges and future directions.

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Abstract:Ontology embeddings map classes, relations, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic $\mathcal{EL}^{++}$, several embedding methods have been developed that explicitly generate models of an ontology. However, these methods suffer from some limitations; they do not distinguish between statements that are unprovable and provably false, and therefore they may use entailed statements as negatives. Furthermore, they do not utilize the deductive closure of an ontology to identify statements that are inferred but not asserted. We evaluated a set of embedding methods for $\mathcal{EL}^{++}$ ontologies based on high-dimensional ball representation of concept descriptions, incorporating several modifications that aim to make use of the ontology deductive closure. In particular, we designed novel negative losses that account both for the deductive closure and different types of negatives. We demonstrate that our embedding methods improve over the baseline ontology embedding in the task of knowledge base or ontology completion.

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Abstract:Generative Adversarial Networks are used for generating the data using a generator and a discriminator, GANs usually produce high-quality images, but training GANs in an adversarial setting is a difficult task. GANs require high computation power and hyper-parameter regularization for converging. Projected GANs tackle the training difficulty of GANs by using transfer learning to project the generated and real samples into a pre-trained feature space. Projected GANs improve the training time and convergence but produce artifacts in the generated images which reduce the quality of the generated samples, we propose an optimized architecture called Stylized Projected GANs which integrates the mapping network of the Style GANs with Skip Layer Excitation of Fast GAN. The integrated modules are incorporated within the generator architecture of the Fast GAN to mitigate the problem of artifacts in the generated images.

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Authors:Tiffany J. Callahan, Ignacio J. Tripodi, Adrianne L. Stefanski, Luca Cappelletti, Sanya B. Taneja, Jordan M. Wyrwa, Elena Casiraghi, Nicolas A. Matentzoglu, Justin Reese, Jonathan C. Silverstein(+22 more)

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Abstract:Translational research requires data at multiple scales of biological organization. Advancements in sequencing and multi-omics technologies have increased the availability of these data but researchers face significant integration challenges. Knowledge graphs (KGs) are used to model complex phenomena, and methods exist to automatically construct them. However, tackling complex biomedical integration problems requires flexibility in the way knowledge is modeled. Moreover, existing KG construction methods provide robust tooling at the cost of fixed or limited choices among knowledge representation models. PheKnowLator (Phenotype Knowledge Translator) is a semantic ecosystem for automating the FAIR (Findable, Accessible, Interoperable, and Reusable) construction of ontologically grounded KGs with fully customizable knowledge representation. The ecosystem includes KG construction resources (e.g., data preparation APIs), analysis tools (e.g., SPARQL endpoints and abstraction algorithms), and benchmarks (e.g., prebuilt KGs and embeddings). We evaluate the ecosystem by surveying open-source KG construction methods and analyzing its computational performance when constructing 12 large-scale KGs. With flexible knowledge representation, PheKnowLator enables fully customizable KGs without compromising performance or usability.

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Abstract:Machine learning with Semantic Web ontologies follows several strategies, one of which involves projecting ontologies into graph structures and applying graph embeddings or graph-based machine learning methods to the resulting graphs. Several methods have been developed that project ontology axioms into graphs. However, these methods are limited in the type of axioms they can project (totality), whether they are invertible (injectivity), and how they exploit semantic information. These limitations restrict the kind of tasks to which they can be applied. Category-theoretical semantics of logic languages formalizes interpretations using categories instead of sets, and categories have a graph-like structure. We developed CatE, which uses the category-theoretical formulation of the semantics of the Description Logic $\mathcal{ALC}$ to generate a graph representation for ontology axioms. The CatE projection is total and injective, and therefore overcomes limitations of other graph-based ontology embedding methods which are generally not invertible. We apply CatE to a number of different tasks, including deductive and inductive reasoning, and we demonstrate that CatE improves over state of the art ontology embedding methods. Furthermore, we show that CatE can also outperform model-theoretic ontology embedding methods in machine learning tasks in the biomedical domain.

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Abstract:Several approaches have been developed that generate embeddings for Description Logic ontologies and use these embeddings in machine learning. One approach of generating ontologies embeddings is by first embedding the ontologies into a graph structure, i.e., introducing a set of nodes and edges for named entities and logical axioms, and then applying a graph embedding to embed the graph in $\mathbb{R}^n$. Methods that embed ontologies in graphs (graph projections) have different formal properties related to the type of axioms they can utilize, whether the projections are invertible or not, and whether they can be applied to asserted axioms or their deductive closure. We analyze, qualitatively and quantitatively, several graph projection methods that have been used to embed ontologies, and we demonstrate the effect of the properties of graph projections on the performance of predicting axioms from ontology embeddings. We find that there are substantial differences between different projection methods, and both the projection of axioms into nodes and edges as well ontological choices in representing knowledge will impact the success of using ontology embeddings to predict axioms.

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Abstract:Many ontologies, i.e., Description Logic (DL) knowledge bases, have been developed to provide rich knowledge about various domains, and a lot of them are based on ALC, i.e., a prototypical and expressive DL, or its extensions. The main task that explores ALC ontologies is to compute semantic entailment. Symbolic approaches can guarantee sound and complete semantic entailment but are sensitive to inconsistency and missing information. To this end, we propose FALCON, a Fuzzy ALC Ontology Neural reasoner. FALCON uses fuzzy logic operators to generate single model structures for arbitrary ALC ontologies, and uses multiple model structures to compute semantic entailments. Theoretical results demonstrate that FALCON is guaranteed to be a sound and complete algorithm for computing semantic entailments over ALC ontologies. Experimental results show that FALCON enables not only approximate reasoning (reasoning over incomplete ontologies) and paraconsistent reasoning (reasoning over inconsistent ontologies), but also improves machine learning in the biomedical domain by incorporating background knowledge from ALC ontologies.

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Abstract:Neural logical reasoning (NLR) is a fundamental task in knowledge discovery and artificial intelligence. NLR aims at answering multi-hop queries with logical operations on structured knowledge bases based on distributed representations of queries and answers. While previous neural logical reasoners can give specific entity-level answers, i.e., perform inductive reasoning from the perspective of logic theory, they are not able to provide descriptive concept-level answers, i.e., perform abductive reasoning, where each concept is a summary of a set of entities. In particular, the abductive reasoning task attempts to infer the explanations of each query with descriptive concepts, which make answers comprehensible to users and is of great usefulness in the field of applied ontology. In this work, we formulate the problem of the joint abductive and inductive neural logical reasoning (AI-NLR), solving which needs to address challenges in incorporating, representing, and operating on concepts. We propose an original solution named ABIN for AI-NLR. Firstly, we incorporate description logic-based ontological axioms to provide the source of concepts. Then, we represent concepts and queries as fuzzy sets, i.e., sets whose elements have degrees of membership, to bridge concepts and queries with entities. Moreover, we design operators involving concepts on top of the fuzzy set representation of concepts and queries for optimization and inference. Extensive experimental results on two real-world datasets demonstrate the effectiveness of ABIN for AI-NLR.

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Authors:Zhenwei Tang, Shichao Pei, Zhao Zhang, Yongchun Zhu, Fuzhen Zhuang, Robert Hoehndorf, Xiangliang Zhang

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Abstract:Most real-world knowledge graphs (KG) are far from complete and comprehensive. This problem has motivated efforts in predicting the most plausible missing facts to complete a given KG, i.e., knowledge graph completion (KGC). However, existing KGC methods suffer from two main issues, 1) the false negative issue, i.e., the candidates for sampling negative training instances include potential true facts; and 2) the data sparsity issue, i.e., true facts account for only a tiny part of all possible facts. To this end, we propose positive-unlabeled learning with adversarial data augmentation (PUDA) for KGC. In particular, PUDA tailors positive-unlabeled risk estimator for the KGC task to deal with the false negative issue. Furthermore, to address the data sparsity issue, PUDA achieves a data augmentation strategy by unifying adversarial training and positive-unlabeled learning under the positive-unlabeled minimax game. Extensive experimental results demonstrate its effectiveness and compatibility.

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Abstract:Many ontologies, in particular in the biomedical domain, are based on the Description Logic EL++. Several efforts have been made to interpret and exploit EL++ ontologies by distributed representation learning. Specifically, concepts within EL++ theories have been represented as n-balls within an n-dimensional embedding space. However, the intersectional closure is not satisfied when using n-balls to represent concepts because the intersection of two n-balls is not an n-ball. This leads to challenges when measuring the distance between concepts and inferring equivalence between concepts. To this end, we developed EL Box Embedding (ELBE) to learn Description Logic EL++ embeddings using axis-parallel boxes. We generate specially designed box-based geometric constraints from EL++ axioms for model training. Since the intersection of boxes remains as a box, the intersectional closure is satisfied. We report extensive experimental results on three datasets and present a case study to demonstrate the effectiveness of the proposed method.

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