随着知识图的扩散，具有复杂多界结构的建模数据在统计关系学习领域获得了越来越大的关注。统计关系学习最重要的目标之一是链路预测，即，预测知识图中是否存在某些关系。已经提出了大量模型和算法来执行链路预测，其中张量分解方法已经证明在计算效率和预测准确性方面实现了最先进的性能。然而，现有张量分解模型的共同缺点是缺失的关系和非现有关系是以相同的方式对待，这导致信息丢失。为了解决这个问题，我们提出了一种具有探测链路的二进制张量分解模型，其不仅继承了来自经典张量分解模型的计算效率，还占关联数据的二进制性质。我们所提出的探测张量分解（PTF）模型显示了预测准确性和可解释性的优点

Relational machine learning studies methods for the statistical analysis of relational, or graph-structured, data. In this paper, we provide a review of how such statistical models can be "trained" on large knowledge graphs, and then used to predict new facts about the world (which is equivalent to predicting new edges in the graph). In particular, we discuss two fundamentally different kinds of statistical relational models, both of which can scale to massive datasets. The first is based on latent feature models such as tensor factorization and multiway neural networks. The second is based on mining observable patterns in the graph. We also show how to combine these latent and observable models to get improved modeling power at decreased computational cost. Finally, we discuss how such statistical models of graphs can be combined with text-based information extraction methods for automatically constructing knowledge graphs from the Web. To this end, we also discuss Google's Knowledge Vault project as an example of such combination.

In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks. 1

Knowledge graph (KG) embedding is to embed components of a KG including entities and relations into continuous vector spaces, so as to simplify the manipulation while preserving the inherent structure of the KG. It can benefit a variety of downstream tasks such as KG completion and relation extraction, and hence has quickly gained massive attention. In this article, we provide a systematic review of existing techniques, including not only the state-of-the-arts but also those with latest trends. Particularly, we make the review based on the type of information used in the embedding task. Techniques that conduct embedding using only facts observed in the KG are first introduced. We describe the overall framework, specific model design, typical training procedures, as well as pros and cons of such techniques. After that, we discuss techniques that further incorporate additional information besides facts. We focus specifically on the use of entity types, relation paths, textual descriptions, and logical rules. Finally, we briefly introduce how KG embedding can be applied to and benefit a wide variety of downstream tasks such as KG completion, relation extraction, question answering, and so forth.

事实证明，信息提取方法可有效从结构化或非结构化数据中提取三重。以（头部实体，关系，尾部实体）形式组织这样的三元组的组织称为知识图（kgs）。当前的大多数知识图都是不完整的。为了在下游任务中使用kgs，希望预测kgs中缺少链接。最近，通过将实体和关系嵌入到低维的矢量空间中，旨在根据先前访问的三元组来预测三元组，从而对KGS表示不同的方法。根据如何独立或依赖对三元组进行处理，我们将知识图完成的任务分为传统和图形神经网络表示学习，并更详细地讨论它们。在传统的方法中，每个三重三倍将独立处理，并在基于GNN的方法中进行处理，三倍也考虑了他们的当地社区。查看全文

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N -way array. Decompositions of higher-order tensors (i.e., N -way arrays with N ≥ 3) have applications in psychometrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

图表可以表示实体之间的关系信息，图形结构广泛用于许多智能任务，例如搜索，推荐和问题应答。然而，实际上大多数图形结构数据都遭受了不完整性，因此链路预测成为一个重要的研究问题。虽然提出了许多模型来用于链路预测，但以下两个问题仍然仍然较少：（1）大多数方法在不利用相关链路中使用丰富的信息，大多数方法都独立模型，并且（2）现有型号主要基于关联设计学习并没有考虑推理。通过这些问题，在本文中，我们提出了图表协作推理（GCR），它可以使用邻居与逻辑推理视角的关系中的关系推理。我们提供了一种简单的方法来将图形结构转换为逻辑表达式，以便链路预测任务可以转换为神经逻辑推理问题。我们应用逻辑受限的神经模块根据逻辑表达式构建网络架构，并使用反向传播以有效地学习模型参数，这在统一架构中桥接可分辨率的学习和象征性推理。为了展示我们工作的有效性，我们对图形相关任务进行实验，例如基于常用的基准数据集的链路预测和推荐，我们的图表合作推理方法实现了最先进的性能。

大型知识图（KGS）提供人类知识的结构化表示。然而，由于不可能包含所有知识，KGs通常不完整。基于现有事实的推理铺平了一种发现缺失事实的方法。在本文中，我们研究了了解完成缺失事实三胞胎的知识图表的推理的学习逻辑规则问题。学习逻辑规则将具有很强的解释性的模型以及概括到类似任务的能力。我们提出了一种称为MPLR的模型，可以改进现有模型以完全使用培训数据，并且考虑多目标方案。此外，考虑到缺乏评估模型表现和开采规则的质量，我们进一步提出了两名新颖的指标来帮助解决问题。实验结果证明我们的MPLR模型在五个基准数据集中优于最先进的方法。结果还证明了指标的有效性。

We consider the problem of embedding entities and relationships of multirelational data in low-dimensional vector spaces. Our objective is to propose a canonical model which is easy to train, contains a reduced number of parameters and can scale up to very large databases. Hence, we propose TransE, a method which models relationships by interpreting them as translations operating on the low-dimensional embeddings of the entities. Despite its simplicity, this assumption proves to be powerful since extensive experiments show that TransE significantly outperforms state-of-the-art methods in link prediction on two knowledge bases. Besides, it can be successfully trained on a large scale data set with 1M entities, 25k relationships and more than 17M training samples.

我们的目标是在沿着张量模式的协变量信息存在中可获得稀疏和高度缺失的张量。我们的动机来自在线广告，在各种设备上的广告上的用户点击率（CTR）形成了大约96％缺失条目的CTR张量，并且在非缺失条目上有许多零，这使得独立的张量完井方法不满意。除了CTR张量旁边，额外的广告功能或用户特性通常可用。在本文中，我们提出了协助协助的稀疏张力完成（Costco），以合并复苏恢复稀疏张量的协变量信息。关键思想是共同提取来自张量和协变矩阵的潜伏组分以学习合成表示。从理论上讲，我们导出了恢复的张量组件的错误绑定，并明确地量化了由于协变量引起的显露概率条件和张量恢复精度的改进。最后，我们将Costco应用于由CTR张量和广告协变矩阵组成的广告数据集，从而通过基线的23％的准确性改进。重要的副产品是来自Costco的广告潜在组件显示有趣的广告集群，这对于更好的广告目标是有用的。

链接预测Infers从观察到的网络中的潜在链接，是网络分析中的基本问题之一。与仅预测双向成对关系的传统图形表示建模相比，我们提出了一种新颖的基于张量的联合网络嵌入方法，同时编码成对链路和超链接到潜在的空间上，从而捕获成对和多向链路之间的依赖性在推断出潜在的未被观察的超链接。所提出的嵌入程序的主要优点是它包括节点之间的成对关系和子组织结构，以捕获更丰富的网络信息。另外，该方法在推断潜在的超链接之间引入了链路之间的分层依赖性，并导致更好的链路预测。理论上，我们建立了拟议的嵌入方法的估计一致性，并提供了与仅利用成对链路或超链接的链路预测相比的更快的收敛速度。与现有链路预测算法相比，仿真设置和Facebook自我网络的数值研究表明，所提出的方法改善了与现有链路预测算法相比的超链接和成对链路预测精度。

最近公布的知识图形嵌入模型的实施，培训和评估的异质性已经公平和彻底的比较困难。为了评估先前公布的结果的再现性，我们在Pykeen软件包中重新实施和评估了21个交互模型。在这里，我们概述了哪些结果可以通过其报告的超参数再现，这只能以备用的超参数再现，并且无法再现，并且可以提供洞察力，以及为什么会有这种情况。然后，我们在四个数据集上进行了大规模的基准测试，其中数千个实验和24,804 GPU的计算时间。我们展示了最佳实践，每个模型的最佳配置以及可以通过先前发布的最佳配置进行改进的洞察。我们的结果强调了模型架构，训练方法，丢失功能和逆关系显式建模的组合对于模型的性能来说至关重要，而不仅由模型架构决定。我们提供了证据表明，在仔细配置时，若干架构可以获得对最先进的结果。我们制定了所有代码，实验配置，结果和分析，导致我们在https://github.com/pykeen/pykeen和https://github.com/pykeen/benchmarking中获得的解释

We estimate the general influence functions for spatio-temporal Hawkes processes using a tensor recovery approach by formulating the location dependent influence function that captures the influence of historical events as a tensor kernel. We assume a low-rank structure for the tensor kernel and cast the estimation problem as a convex optimization problem using the Fourier transformed nuclear norm (TNN). We provide theoretical performance guarantees for our approach and present an algorithm to solve the optimization problem. Moreover, we demonstrate the efficiency of our estimation with numerical simulations.

知识图表（KGS）是真实世界事实的结构化表示，是融合人类知识的智能数据库，可以帮助机器模仿人类问题的方法。然而，由于快速迭代的性质以及数据的不完整，KGs通常是巨大的，并且在公斤上有不可避免的事实。对于知识图链接的预测是针对基于现有的知识推理来完成缺少事实的任务。广泛研究了两个主要的研究流：一个学习可以捕获潜在模式的实体和关系的低维嵌入，以及通过采矿逻辑规则的良好解释性。不幸的是，以前的研究很少关注异质的KG。在本文中，我们提出了一种将基于嵌入的学习和逻辑规则挖掘结合的模型，以推断在KG上。具体地，我们研究了从节点程度的角度涉及各种类型的实体和关系的异构kg中的缺失链接的问题。在实验中，我们证明了我们的DegreEmbed模型优于对现实世界的数据集的国家的最先进的方法。同时，我们模型开采的规则具有高质量和可解释性。

我们使用张量奇异值分解（T-SVD）代数框架提出了一种新的快速流算法，用于抵抗缺失的低管级张量的缺失条目。我们展示T-SVD是三阶张量的研究型块术语分解的专业化，我们在该模型下呈现了一种算法，可以跟踪从不完全流2-D数据的可自由子模块。所提出的算法使用来自子空间的基层歧管的增量梯度下降的原理，以解决线性复杂度和时间样本的恒定存储器的张量完成问题。我们为我们的算法提供了局部预期的线性收敛结果。我们的经验结果在精确态度上具有竞争力，但在计算时间内比实际应用上的最先进的张量完成算法更快，以在有限的采样下恢复时间化疗和MRI数据。

We study the problem of learning representations of entities and relations in knowledge graphs for predicting missing links. The success of such a task heavily relies on the ability of modeling and inferring the patterns of (or between) the relations. In this paper, we present a new approach for knowledge graph embedding called RotatE, which is able to model and infer various relation patterns including: symmetry/antisymmetry, inversion, and composition. Specifically, the RotatE model defines each relation as a rotation from the source entity to the target entity in the complex vector space. In addition, we propose a novel self-adversarial negative sampling technique for efficiently and effectively training the RotatE model. Experimental results on multiple benchmark knowledge graphs show that the proposed RotatE model is not only scalable, but also able to infer and model various relation patterns and significantly outperform existing state-of-the-art models for link prediction.

捕获关系的构图模式是知识图表完成中的重要任务。它还是迈向多跳推理的基本步骤，以了解学到的知识。以前，已经开发了几种基于旋转的翻译方法来使用一系列复值对角线矩阵的产品来模拟复合关系。然而，这些方法倾向于对复合关系进行几种超薄假设，例如，强迫他们独立于实体和缺乏语义等级的交换。为了系统地解决这些问题，我们开发了一种新颖的知识图形嵌入方法，命名为密集，为复杂的关系模式提供改进的建模方案。特别地，我们的方法将每个关系分解成SO（3）基于基于组的旋转操作员和三维（3-D）欧几里德空间中的缩放操作员。这种设计原理导致我们的方法的几个优点：（1）对于复合关系，相应的对角线关系矩阵可以是非换向的，反映了现实世界应用中的主要情景; （2）我们的模型保留了关系运营和实体嵌入之间的自然互动; （3）缩放操作为实体的内在语义层次结构提供建模电力; （4）在参数大小和培训时间方面，以高计算效率实现致密的增强效果; （5）欧几里德空间中的建模实体而不是四元数空间，保持关系模式的直接几何解释。多个基准知识图上的实验结果表明，密集优于当前最先进的模型，以缺少链路预测，尤其是对复合关系。

This paper presents a machine learning approach to multidimensional item response theory (MIRT), a class of latent factor models that can be used to model and predict student performance from observed assessment data. Inspired by collaborative filtering, we define a general class of models that includes many MIRT models. We discuss the use of penalized joint maximum likelihood (JML) to estimate individual models and cross-validation to select the best performing model. This model evaluation process can be optimized using batching techniques, such that even sparse large-scale data can be analyzed efficiently. We illustrate our approach with simulated and real data, including an example from a massive open online course (MOOC). The high-dimensional model fit to this large and sparse dataset does not lend itself well to traditional methods of factor interpretation. By analogy to recommender-system applications, we propose an alternative "validation" of the factor model, using auxiliary information about the popularity of items consulted during an open-book exam in the course.

Knowledge graphs enable a wide variety of applications, including question answering and information retrieval. Despite the great effort invested in their creation and maintenance, even the largest (e.g., Yago, DBPedia or Wikidata) remain incomplete. We introduce Relational Graph Convolutional Networks (R-GCNs) and apply them to two standard knowledge base completion tasks: Link prediction (recovery of missing facts, i.e. subject-predicate-object triples) and entity classification (recovery of missing entity attributes). R-GCNs are related to a recent class of neural networks operating on graphs, and are developed specifically to deal with the highly multi-relational data characteristic of realistic knowledge bases. We demonstrate the effectiveness of R-GCNs as a stand-alone model for entity classification. We further show that factorization models for link prediction such as DistMult can be significantly improved by enriching them with an encoder model to accumulate evidence over multiple inference steps in the relational graph, demonstrating a large improvement of 29.8% on FB15k-237 over a decoder-only baseline. * Equal contribution.

Knowledge bases are an important resource for question answering and other tasks but often suffer from incompleteness and lack of ability to reason over their discrete entities and relationships. In this paper we introduce an expressive neural tensor network suitable for reasoning over relationships between two entities. Previous work represented entities as either discrete atomic units or with a single entity vector representation. We show that performance can be improved when entities are represented as an average of their constituting word vectors. This allows sharing of statistical strength between, for instance, facts involving the "Sumatran tiger" and "Bengal tiger." Lastly, we demonstrate that all models improve when these word vectors are initialized with vectors learned from unsupervised large corpora. We assess the model by considering the problem of predicting additional true relations between entities given a subset of the knowledge base. Our model outperforms previous models and can classify unseen relationships in WordNet and FreeBase with an accuracy of 86.2% and 90.0%, respectively.