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Knowledge Graph Embeddings in Geometric Algebras

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 Added by Chengjin Xu
 Publication date 2020
and research's language is English




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Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a lowdimensional latent representation space. Existing KG embedding approaches model entities andrelations in a KG by utilizing real-valued , complex-valued, or hypercomplex-valued (Quaternionor Octonion) representations, all of which are subsumed into a geometric algebra. In this work,we introduce a novel geometric algebra-based KG embedding framework, GeomE, which uti-lizes multivector representations and the geometric product to model entities and relations. Ourframework subsumes several state-of-the-art KG embedding approaches and is advantageouswith its ability of modeling various key relation patterns, including (anti-)symmetry, inversionand composition, rich expressiveness with higher degree of freedom as well as good general-ization capacity. Experimental results on multiple benchmark knowledge graphs show that theproposed approach outperforms existing state-of-the-art models for link prediction.



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Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical data, hyperbolic embedding methods have shown promise for high-fidelity and parsimonious representations. However, existing hyperbolic embedding methods do not account for the rich logical patterns in KGs. In this work, we introduce a class of hyperbolic KG embedding models that simultaneously capture hierarchical and logical patterns. Our approach combines hyperbolic reflections and rotations with attention to model complex relational patterns. Experimental results on standard KG benchmarks show that our method improves over previous Euclidean- and hyperbolic-based efforts by up to 6.1% in mean reciprocal rank (MRR) in low dimensions. Furthermore, we observe that different geometric transformations capture different types of relations while attention-based transformations generalize to multiple relations. In high dimensions, our approach yields new state-of-the-art MRRs of 49.6% on WN18RR and 57.7% on YAGO3-10.
154 - Zequn Sun , Muhao Chen , Wei Hu 2020
Capturing associations for knowledge graphs (KGs) through entity alignment, entity type inference and other related tasks benefits NLP applications with comprehensive knowledge representations. Recent related methods built on Euclidean embeddings are challenged by the hierarchical structures and different scales of KGs. They also depend on high embedding dimensions to realize enough expressiveness. Differently, we explore with low-dimensional hyperbolic embeddings for knowledge association. We propose a hyperbolic relational graph neural network for KG embedding and capture knowledge associations with a hyperbolic transformation. Extensive experiments on entity alignment and type inference demonstrate the effectiveness and efficiency of our method.
Knowledge graph embeddings rank among the most successful methods for link prediction in knowledge graphs, i.e., the task of completing an incomplete collection of relational facts. A downside of these models is their strong sensitivity to model hyperparameters, in particular regularizers, which have to be extensively tuned to reach good performance [Kadlec et al., 2017]. We propose an efficient method for large scale hyperparameter tuning by interpreting these models in a probabilistic framework. After a model augmentation that introduces per-entity hyperparameters, we use a variational expectation-maximization approach to tune thousands of such hyperparameters with minimal additional cost. Our approach is agnostic to details of the model and results in a new state of the art in link prediction on standard benchmark data.
Interference between pharmacological substances can cause serious medical injuries. Correctly predicting so-called drug-drug interactions (DDI) does not only reduce these cases but can also result in a reduction of drug development cost. Presently, most drug-related knowledge is the result of clinical evaluations and post-marketing surveillance; resulting in a limited amount of information. Existing data-driven prediction approaches for DDIs typically rely on a single source of information, while using information from multiple sources would help improve predictions. Machine learning (ML) techniques are used, but the techniques are often unable to deal with skewness in the data. Hence, we propose a new ML approach for predicting DDIs based on multiple data sources. For this task, we use 12,000 drug features from DrugBank, PharmGKB, and KEGG drugs, which are integrated using Knowledge Graphs (KGs). To train our prediction model, we first embed the nodes in the graph using various embedding approaches. We found that the best performing combination was a ComplEx embedding method creating using PyTorch-BigGraph (PBG) with a Convolutional-LSTM network and classic machine learning-based prediction models. The model averaging ensemble method of three best classifiers yields up to 0.94, 0.92, 0.80 for AUPR, F1-score, and MCC, respectively during 5-fold cross-validation tests.
Interaction between pharmacological agents can trigger unexpected adverse events. Capturing richer and more comprehensive information about drug-drug interactions (DDI) is one of the key tasks in public health and drug development. Recently, several knowledge graph embedding approaches have received increasing attention in the DDI domain due to their capability of projecting drugs and interactions into a low-dimensional feature space for predicting links and classifying triplets. However, existing methods only apply a uniformly random mode to construct negative samples. As a consequence, these samples are often too simplistic to train an effective model. In this paper, we propose a new knowledge graph embedding framework by introducing adversarial autoencoders (AAE) based on Wasserstein distances and Gumbel-Softmax relaxation for drug-drug interactions tasks. In our framework, the autoencoder is employed to generate high-quality negative samples and the hidden vector of the autoencoder is regarded as a plausible drug candidate. Afterwards, the discriminator learns the embeddings of drugs and interactions based on both positive and negative triplets. Meanwhile, in order to solve vanishing gradient problems on the discrete representation--an inherent flaw in traditional generative models--we utilize the Gumbel-Softmax relaxation and the Wasserstein distance to train the embedding model steadily. We empirically evaluate our method on two tasks, link prediction and DDI classification. The experimental results show that our framework can attain significant improvements and noticeably outperform competitive baselines.

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