This paper tackles the problem of endogenous link prediction for Knowledge Base completion. Knowledge Bases can be represented as directed graphs whose nodes correspond to entities and edges to relationships. Previous attempts either consist of powerful systems with high capacity to model complex connectivity patterns, which unfortunately usually end up overfitting on rare relationships, or in approaches that trade capacity for simplicity in order to fairly model all relationships, frequent or not. In this paper, we propose Tatec a happy medium obtained by complementing a high-capacity model with a simpler one, both pre-trained separately and then combined. We present several variants of this model with different kinds of regularization and combination strategies and show that this approach outperforms existing methods on different types of relationships by achieving state-of-the-art results on four benchmarks of the literature.
While there has been a lot of focus recently on algorithms purely based on learning embeddings for entities and or relationships, many earlier alternatives had been proposed. We discuss works carried ou in the Bayesian clustering framework, as well as approaches that explicitly use the graph structure of the data. The Infinite Relational Model of @cite_18 , which is a nonparametric extension of the Stochastic Blockmodel @cite_11 , is a Bayesian clustering approach that learns clusters of entities of the same kind, i.e. groups of entities that can have similar relationships with other entities. This work was followed by @cite_1 , a 3-way tensor factorization model based on Bayesian clustering in which entities within a cluster share the same distribution of embeddings.
@cite_18 @cite_1 @cite_11
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We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (, 2013) and TransE (, 2013b), can be generalized under a unified learning framework, where entities are low-dimensional vectors learned from a neural network and relations are bilinear and or linear mapping functions. Under this framework, we compare a variety of embedding models on the link prediction task. We show that a simple bilinear formulation achieves new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2 vs. 54.7 by TransE on Freebase). Furthermore, we introduce a novel approach that utilizes the learned relation embeddings to mine logical rules such as "BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that embeddings learned from the bilinear objective are particularly good at capturing relational semantics and that the composition of relations is characterized by matrix multiplication. More interestingly, we demonstrate that our embedding-based rule extraction approach successfully outperforms a state-of-the-art confidence-based rule mining approach in mining Horn rules that involve compositional reasoning. Abstract: We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (, 2013) and TransE (, 2013b), can be generalized under a unified learning framework, where entities are low-dimensional vectors learned from a neural network and relations are bilinear and or linear mapping functions. Under this framework, we compare a variety of embedding models on the link prediction task. We show that a simple bilinear formulation achieves new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2 vs. 54.7 by TransE on Freebase). Furthermore, we introduce a novel approach that utilizes the learned relation embeddings to mine logical rules such as "BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that embeddings learned from the bilinear objective are particularly good at capturing relational semantics and that the composition of relations is characterized by matrix multiplication. More interestingly, we demonstrate that our embedding-based rule extraction approach successfully outperforms a state-of-the-art confidence-based rule mining approach in mining Horn rules that involve compositional reasoning. As the availability and importance of relational data—such as the friendships summarized on a social networking website—increases, it becomes increasingly important to have good models for such data. The kinds of latent structure that have been considered for use in predicting links in such networks have been relatively limited. In particular, the machine learning community has focused on latent class models, adapting Bayesian nonparametric methods to jointly infer how many latent classes there are while learning which entities belong to each class. We pursue a similar approach with a richer kind of latent variable—latent features—using a Bayesian nonparametric approach to simultaneously infer the number of features at the same time we learn which entities have each feature. Our model combines these inferred features with known covariates in order to perform link prediction. We demonstrate that the greater expressiveness of this approach allows us to improve performance on three datasets. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior “landscape”. We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach. In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A standard approach is to classify each entity independently, ignoring the correlations between them. Recently, Probabilistic Relational Models, a relational version of Bayesian networks, were used to define a joint probabilistic model for a collection of related entities. In this paper, we present an alternative framework that builds on (conditional) Markov networks and addresses two limitations of the previous approach. First, undirected models do not impose the acyclicity constraint that hinders representation of many important relational dependencies in directed models. Second, undirected models are well suited for discriminative training, where we optimize the conditional likelihood of the labels given the features, which generally improves classification accuracy. We show how to train these models effectively, and how to use approximate probabilistic inference over the learned model for collective classification of multiple related entities. We provide experimental results on a webpage classification task, showing that accuracy can be significantly improved by modeling relational dependencies. These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental in the quantification of uncertainty within applications in volving the blending of mathematical models with data. The finite dimensional situation is described first, along with some motivational examples. Then the development of probability measures on separable Banach space is undertaken, using a random series over an infinite set of functions to construct draws; these probability measures are used as priors in the Bayesian approach to inverse problems. Regularity of draws from the priors is studied in the natural Sobolev or Besov spaces implied by the choice of functions in the random series construction, and the Kolmogorov continuity theorem is used to extend regularity considerations to the space of Holder continuous functions. Bayes’ theorem is de rived in this prior setting, and here interpreted as finding conditions under which the posterior is absolutely continuous with respect to the prior, and determining a formula for the Radon-Nikodym derivative in terms of the likelihood of the data. Having established the form of the posterior, we then describe various properties common to it in the infinite dimensional setting. These properties include well-posedness, approximation theory, and the existence of maximum a posteriori estimators. We then describe measure-preserving dynamics, again on the infinite dimensional space, including Markov chain-Monte C arlo and sequential Monte Carlo methods, and measure-preserving reversible stochastic differential equations. By formulating the theory and algorithms on the underlying infinite dimensional space, we obtain a framework suitable for rigorous analysis of the accuracy of reconstructions, of computational complexity, as well as naturally constructing algorithms which perform well under mesh refinement, since they are inherently well-defined in infinite dimensions. We consider the problem of learning probabilistic models for complex relational structures between various types of objects. A model can help us "understand" a dataset of relational facts in at least two ways, by finding interpretable structure in the data, and by supporting predictions, or inferences about whether particular unobserved relations are likely to be true. Often there is a tradeoff between these two aims: cluster-based models yield more easily interpretable representations, while factorization-based approaches have given better predictive performance on large data sets. We introduce the Bayesian Clustered Tensor Factorization (BCTF) model, which embeds a factorized representation of relations in a nonparametric Bayesian clustering framework. Inference is fully Bayesian but scales well to large data sets. The model simultaneously discovers interpretable clusters and yields predictive performance that matches or beats previous probabilistic models for relational data. Bayesian models offer great flexibility for clustering applications---Bayesian nonparametrics can be used for modeling infinite mixtures, and hierarchical Bayesian models can be utilized for sharing clusters across multiple data sets. For the most part, such flexibility is lacking in classical clustering methods such as k-means. In this paper, we revisit the k-means clustering algorithm from a Bayesian nonparametric viewpoint. Inspired by the asymptotic connection between k-means and mixtures of Gaussians, we show that a Gibbs sampling algorithm for the Dirichlet process mixture approaches a hard clustering algorithm in the limit, and further that the resulting algorithm monotonically minimizes an elegant underlying k-means-like clustering objective that includes a penalty for the number of clusters. We generalize this analysis to the case of clustering multiple data sets through a similar asymptotic argument with the hierarchical Dirichlet process. We also discuss further extensions that highlight the benefits of our analysis: i) a spectral relaxation involving thresholded eigenvectors, and ii) a normalized cut graph clustering algorithm that does not fix the number of clusters in the graph. We consider the statistical analysis of a collection of unipartite graphs, i.e., multiple matrices of relations among objects of a single type. Such data arise, for example, in biological settings, collections of author-recipient email, and social networks. In many applications, clustering the objects of study or situating them in a low dimensional space (e.g., a simplex) is only one of the goals of the analysis. Begin able to estimate relational structures among the clusters themselves is often times as important. For example, in biological applications we are interested in estimating how stable protein complexes (i.e., clusters of proteins) interact. To support such integrated data analyses, we develop the family of “stochastic block models of mixed membership”. Our models combine features of mixed-membership models (Erosheva & Fienberg, 2005) and block models for relational data (, 1983) in a hierarchical Bayesian framework. We develop a novel “nested” variational inference scheme, which is necessary to successfully perform fast approximate posterior inference in our models of relational data. We present evidence to support our claims, using both synthetic data and biological case study. We propose an efficient Bayesian nonparametric model for discovering hierarchical community structure in social networks. Our model is a tree-structured mixture of potentially exponentially many stochastic blockmodels. We describe a family of greedy agglomerative model selection algorithms that take just one pass through the data to learn a fully probabilistic, hierarchical community model. In the worst case, Our algorithms scale quadratically in the number of vertices of the network, but independent of the number of nested communities. In practice, the run time of our algorithms are two orders of magnitude faster than the Infinite Relational Model, achieving comparable or better accuracy. This paper examines how a new class of nonparametric Bayesian models can be effectively applied to an open-domain event coreference task. Designed with the purpose of clustering complex linguistic objects, these models consider a potentially infinite number of features and categorical outcomes. The evaluation performed for solving both within- and cross-document event coreference shows significant improvements of the models when compared against two baselines for this task. This paper introduces LDA-G, a scalable Bayesian approach to finding latent group structures in large real-world graph data. Existing Bayesian approaches for group discovery (such as Infinite Relational Models) have only been applied to small graphs with a couple of hundred nodes. LDA-G (short for Latent Dirichlet Allocation for Graphs) utilizes a well-known topic modeling algorithm to find latent group structure. Specifically, we modify Latent Dirichlet Allocation (LDA) to operate on graph data instead of text corpora. Our modifications reflect the differences between real-world graph data and text corpora (e.g., a node's neighbor count vs. a document's word count). In our empirical study, we apply LDA-G to several large graphs (with thousands of nodes) from PubMed (a scientific publication repository). We compare LDA-G's quantitative performance on link prediction with two existing approaches: one Bayesian (namely, Infinite Relational Model) and one non-Bayesian (namely, Cross-association). On average, LDA-G outperforms IRM by 15 and Cross-association by 25 (in terms of area under the ROC curve). Furthermore, we demonstrate that LDA-G can discover useful qualitative information. We present an unsupervised, nonparametric Bayesian approach to coreference resolution which models both global entity identity across a corpus as well as the sequential anaphoric structure within each document. While most existing coreference work is driven by pairwise decisions, our model is fully generative, producing each mention from a combination of global entity properties and local attentional state. Despite being unsupervised, our system achieves a 70.3 MUC F1 measure on the MUC-6 test set, broadly in the range of some recent supervised results. Representing entities and relations in an embedding space is a well-studied approach for machine learning on relational data. Existing approaches however primarily focus on simple link structure between a finite set of entities, ignoring the variety of data types that are often used in relational databases, such as text, images, and numerical values. In our approach, we propose a multimodal embedding using different neural encoders for this variety of data, and combine with existing models to learn embeddings of the entities. We extend existing datasets to create two novel benchmarks, YAGO-10-plus and MovieLens-100k-plus, that contain additional relations such as textual descriptions and images of the original entities. We demonstrate that our model utilizes the additional information effectively to provide further gains in accuracy. Moreover, we test our learned multimodal embeddings by using them to predict missing multimodal attributes. This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the condition of separate exchangeability. We provide oracle inequalities with rate of convergence @math corresponding to profile likelihood maximization and mean-square error minimization, and show that the blockmodel can be interpreted in this setting as an optimal piecewise-constant approximation to the generative nonparametric model. We also show for large sample sizes that the detection of co-clusters in such data indicates with high probability the existence of co-clusters of equal size and asymptotically equivalent connectivity in the underlying generative process. We present a new method for clustering based on compression. The method does not use subject-specific features or background knowledge, and works as follows: First, we determine a parameter-free, universal, similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal. However, the optimality comes at the price of using the noncomputable notion of Kolmogorov complexity. We propose axioms to capture the real-world setting, and show that the NCD approximates optimality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (ternary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics, we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis. The binary symmetric stochastic block model deals with a random graph of @math vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability @math within clusters and @math across clusters. In the asymptotic regime of @math and @math for fixed @math and @math , we show that the semidefinite programming relaxation of the maximum likelihood estimator achieves the optimal threshold for exactly recovering the partition from the graph with probability tending to one, resolving a conjecture of Abbe14 . Furthermore, we show that the semidefinite programming relaxation also achieves the optimal recovery threshold in the planted dense subgraph model containing a single cluster of size proportional to @math . We compare the three basic algorithms for model-based clustering on high-dimensional discrete-variable datasets. All three algorithms use the same underlying model: a naive-Bayes model with a hidden root node, also known as a multinomial-mixture model. In the first part of the paper, we perform an experimental comparison between three batch algorithms that learn the parameters of this model: the Expectation–Maximization (EM) algorithm, a “winner take all” version of the EM algorithm reminiscent of the K-means algorithm, and model-based agglomerative clustering. We find that the EM algorithm significantly outperforms the other methods, and proceed to investigate the effect of various initialization methods on the final solution produced by the EM algorithm. The initializations that we consider are (1) parameters sampled from an uninformative prior, (2) random perturbations of the marginal distribution of the data, and (3) the output of agglomerative clustering. Although the methods are substantially different, they lead to learned models that are similar in quality. Vast amounts of structured information have been published in the Semantic Web's Linked Open Data (LOD) cloud and their size is still growing rapidly. Yet, access to this information via reasoning and querying is sometimes difficult, due to LOD's size, partial data inconsistencies and inherent noisiness. Machine Learning offers an alternative approach to exploiting LOD's data with the advantages that Machine Learning algorithms are typically robust to both noise and data inconsistencies and are able to efficiently utilize non-deterministic dependencies in the data. From a Machine Learning point of view, LOD is challenging due to its relational nature and its scale. Here, we present an efficient approach to relational learning on LOD data, based on the factorization of a sparse tensor that scales to data consisting of millions of entities, hundreds of relations and billions of known facts. Furthermore, we show how ontological knowledge can be incorporated in the factorization to improve learning results and how computation can be distributed across multiple nodes. We demonstrate that our approach is able to factorize the YAGO 2 core ontology and globally predict statements for this large knowledge base using a single dual-core desktop computer. Furthermore, we show experimentally that our approach achieves good results in several relational learning tasks that are relevant to Linked Data. Once a factorization has been computed, our model is able to predict efficiently, and without any additional training, the likelihood of any of the 4.3 ⋅ 1014 possible triples in the YAGO 2 core ontology. We examine the embedding approach to reason new relational facts from a largescale knowledge graph and a text corpus. We propose a novel method of jointly embedding entities and words into the same continuous vector space. The embedding process attempts to preserve the relations between entities in the knowledge graph and the concurrences of words in the text corpus. Entity names and Wikipedia anchors are utilized to align the embeddings of entities and words in the same space. Large scale experiments on Freebase and a Wikipedia NY Times corpus show that jointly embedding brings promising improvement in the accuracy of predicting facts, compared to separately embedding knowledge graphs and text. Particularly, jointly embedding enables the prediction of facts containing entities out of the knowledge graph, which cannot be handled by previous embedding methods. At the same time, concerning the quality of the word embeddings, experiments on the analogical reasoning task show that jointly embedding is comparable to or slightly better than word2vec (Skip-Gram).