Integrating prior knowledge into factorization approaches for relational learning

An efficient way to represent the domain knowledge is relational data, where information is recorded in form of relationships between entities. Relational data is becoming ubiquitous over the years for knowledge representation due to the fact that many real-word data is inherently interlinked. Some well-known examples of relational data are: the World Wide Web (WWW), a system of interlinked hypertext documents; the Linked Open Data (LOD) cloud of the Semantic Web, a collection of published data and their interlinks; and finally the Internet of Things (IoT), a network of physical objects with internal states and communications ability. Relational data has been addressed by many different machine learning approaches, the most promising ones are in the area of relational learning, which is the focus of this thesis. While conventional machine learning algorithms consider entities as being independent instances randomly sampled from some statistical distribution and being represented as data points in a vector space, relational learning takes into account the overall network environment when predicting the label of an entity, an attribute value of an entity or the existence of a relationship between entities. An important feature is that relational learning can exploit contextual information that is more distant in the relational network. As the volume and structural complexity of the relational data increase constantly in the era of Big Data, scalability and the modeling power become crucial for relational learning algorithms. Previous relational learning algorithms either provide an intuitive representation of the model, such as Inductive Logic Programming (ILP) and Markov Logic Networks (MLNs), or assume a set of latent variables to explain the observed data, such as the Infinite Hidden Relational Model (IHRM), the Infinite Relational Model (IRM) and factorization approaches. Models with intuitive representations often involve some form of structure learning which leads to scalability problems due to a typically large search space. Factorizations are among the best-performing approaches for large-scale relational learning since the algebraic computations can easily be parallelized and since they can exploit data sparsity. Previous factorization approaches exploit only patterns in the relational data itself and the focus of the thesis is to investigate how additional prior information (comprehensive information), either in form of unstructured data (e.g., texts) or structured patterns (e.g., in form of rules) can be considered in the factorization approaches. The goal is to enhance the predictive power of factorization approaches by involving prior knowledge for the learning, and on the other hand to reduce the model complexity for efficient learning. This thesis contains two main contributions: The first contribution presents a general and novel framework for predicting relationships in multirelational data using a set of matrices describing the various instantiated relations in the network. The instantiated relations, derived or learnt from prior knowledge, are integrated as entities' attributes or entity-pairs' attributes into different adjacency matrices for the learning. All the information available is then combined in an additive way. Efficient learning is achieved using an alternating least squares approach exploiting sparse matrix algebra and low-rank approximation. As an illustration, several algorithms are proposed to include information extraction, deductive reasoning and contextual information in matrix factorizations for the Semantic Web scenario and for recommendation systems. Experiments on various data sets are conducted for each proposed algorithm to show the improvement in predictive power by combining matrix factorizations with prior knowledge in a modular way. In contrast to a matrix, a 3-way tensor si a more natural representation for the multirelational data where entities are connected by different types of relations. A 3-way tensor is a three dimensional array which represents the multirelational data by using the first two dimensions for entities and using the third dimension for different types of relations. In the thesis, an analysis on the computational complexity of tensor models shows that the decomposition rank is key for the success of an efficient tensor decomposition algorithm, and that the factorization rank can be reduced by including observable patterns. Based on these theoretical considerations, a second contribution of this thesis develops a novel tensor decomposition approach - an Additive Relational Effects (ARE) model - which combines the strengths of factorization approaches and prior knowledge in an additive way to discover different relational effects from the relational data. As a result, ARE consists of a decomposition part which derives the strong relational leaning effects from a highly scalable tensor decomposition approach RESCAL and a Tucker 1 tensor which integrates the prior knowledge as instantiated relations. An efficient least squares approach is proposed to compute the combined model ARE. The additive model contains weights that reflect the degree of reliability of the prior knowledge, as evaluated by the data. Experiments on several benchmark data sets show that the inclusion of prior knowledge can lead to better performing models at a low tensor rank, with significant benefits for run-time and storage requirements. In particular, the results show that ARE outperforms state-of-the-art relational learning algorithms including intuitive models such as MRC, which is an approach based on Markov Logic with structure learning, factorization approaches such as Tucker, CP, Bayesian Clustered Tensor Factorization (BCTF), the Latent Factor Model (LFM), RESCAL, and other latent models such as the IRM. A final experiment on a Cora data set for paper topic classification shows the improvement of ARE over RESCAL in both predictive power and runtime performance, since ARE requires a significantly lower rank

Holographic Embeddings of Knowledge Graphs

Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn compositional vector space representations of entire knowledge graphs. The proposed method is related to holographic models of associative memory in that it employs circular correlation to create compositional representations. By using correlation as the compositional operator HolE can capture rich interactions but simultaneously remains efficient to compute, easy to train, and scalable to very large datasets. In extensive experiments we show that holographic embeddings are able to outperform state-of-the-art methods for link prediction in knowledge graphs and relational learning benchmark datasets.Comment: To appear in AAAI-1

Type-Constrained Representation Learning in Knowledge Graphs

Large knowledge graphs increasingly add value to various applications that require machines to recognize and understand queries and their semantics, as in search or question answering systems. Latent variable models have increasingly gained attention for the statistical modeling of knowledge graphs, showing promising results in tasks related to knowledge graph completion and cleaning. Besides storing facts about the world, schema-based knowledge graphs are backed by rich semantic descriptions of entities and relation-types that allow machines to understand the notion of things and their semantic relationships. In this work, we study how type-constraints can generally support the statistical modeling with latent variable models. More precisely, we integrated prior knowledge in form of type-constraints in various state of the art latent variable approaches. Our experimental results show that prior knowledge on relation-types significantly improves these models up to 77% in link-prediction tasks. The achieved improvements are especially prominent when a low model complexity is enforced, a crucial requirement when these models are applied to very large datasets. Unfortunately, type-constraints are neither always available nor always complete e.g., they can become fuzzy when entities lack proper typing. We show that in these cases, it can be beneficial to apply a local closed-world assumption that approximates the semantics of relation-types based on observations made in the data

Integrating prior knowledge into factorization approaches for relational learning

An efficient way to represent the domain knowledge is relational data, where information is recorded in form of relationships between entities. Relational data is becoming ubiquitous over the years for knowledge representation due to the fact that many real-word data is inherently interlinked. Some well-known examples of relational data are: the World Wide Web (WWW), a system of interlinked hypertext documents; the Linked Open Data (LOD) cloud of the Semantic Web, a collection of published data and their interlinks; and finally the Internet of Things (IoT), a network of physical objects with internal states and communications ability. Relational data has been addressed by many different machine learning approaches, the most promising ones are in the area of relational learning, which is the focus of this thesis. While conventional machine learning algorithms consider entities as being independent instances randomly sampled from some statistical distribution and being represented as data points in a vector space, relational learning takes into account the overall network environment when predicting the label of an entity, an attribute value of an entity or the existence of a relationship between entities. An important feature is that relational learning can exploit contextual information that is more distant in the relational network. As the volume and structural complexity of the relational data increase constantly in the era of Big Data, scalability and the modeling power become crucial for relational learning algorithms. Previous relational learning algorithms either provide an intuitive representation of the model, such as Inductive Logic Programming (ILP) and Markov Logic Networks (MLNs), or assume a set of latent variables to explain the observed data, such as the Infinite Hidden Relational Model (IHRM), the Infinite Relational Model (IRM) and factorization approaches. Models with intuitive representations often involve some form of structure learning which leads to scalability problems due to a typically large search space. Factorizations are among the best-performing approaches for large-scale relational learning since the algebraic computations can easily be parallelized and since they can exploit data sparsity. Previous factorization approaches exploit only patterns in the relational data itself and the focus of the thesis is to investigate how additional prior information (comprehensive information), either in form of unstructured data (e.g., texts) or structured patterns (e.g., in form of rules) can be considered in the factorization approaches. The goal is to enhance the predictive power of factorization approaches by involving prior knowledge for the learning, and on the other hand to reduce the model complexity for efficient learning. This thesis contains two main contributions: The first contribution presents a general and novel framework for predicting relationships in multirelational data using a set of matrices describing the various instantiated relations in the network. The instantiated relations, derived or learnt from prior knowledge, are integrated as entities' attributes or entity-pairs' attributes into different adjacency matrices for the learning. All the information available is then combined in an additive way. Efficient learning is achieved using an alternating least squares approach exploiting sparse matrix algebra and low-rank approximation. As an illustration, several algorithms are proposed to include information extraction, deductive reasoning and contextual information in matrix factorizations for the Semantic Web scenario and for recommendation systems. Experiments on various data sets are conducted for each proposed algorithm to show the improvement in predictive power by combining matrix factorizations with prior knowledge in a modular way. In contrast to a matrix, a 3-way tensor si a more natural representation for the multirelational data where entities are connected by different types of relations. A 3-way tensor is a three dimensional array which represents the multirelational data by using the first two dimensions for entities and using the third dimension for different types of relations. In the thesis, an analysis on the computational complexity of tensor models shows that the decomposition rank is key for the success of an efficient tensor decomposition algorithm, and that the factorization rank can be reduced by including observable patterns. Based on these theoretical considerations, a second contribution of this thesis develops a novel tensor decomposition approach - an Additive Relational Effects (ARE) model - which combines the strengths of factorization approaches and prior knowledge in an additive way to discover different relational effects from the relational data. As a result, ARE consists of a decomposition part which derives the strong relational leaning effects from a highly scalable tensor decomposition approach RESCAL and a Tucker 1 tensor which integrates the prior knowledge as instantiated relations. An efficient least squares approach is proposed to compute the combined model ARE. The additive model contains weights that reflect the degree of reliability of the prior knowledge, as evaluated by the data. Experiments on several benchmark data sets show that the inclusion of prior knowledge can lead to better performing models at a low tensor rank, with significant benefits for run-time and storage requirements. In particular, the results show that ARE outperforms state-of-the-art relational learning algorithms including intuitive models such as MRC, which is an approach based on Markov Logic with structure learning, factorization approaches such as Tucker, CP, Bayesian Clustered Tensor Factorization (BCTF), the Latent Factor Model (LFM), RESCAL, and other latent models such as the IRM. A final experiment on a Cora data set for paper topic classification shows the improvement of ARE over RESCAL in both predictive power and runtime performance, since ARE requires a significantly lower rank

Open-Vocabulary Semantic Parsing with both Distributional Statistics and Formal Knowledge

Traditional semantic parsers map language onto compositional, executable queries in a fixed schema. This mapping allows them to effectively leverage the information contained in large, formal knowledge bases (KBs, e.g., Freebase) to answer questions, but it is also fundamentally limiting---these semantic parsers can only assign meaning to language that falls within the KB's manually-produced schema. Recently proposed methods for open vocabulary semantic parsing overcome this limitation by learning execution models for arbitrary language, essentially using a text corpus as a kind of knowledge base. However, all prior approaches to open vocabulary semantic parsing replace a formal KB with textual information, making no use of the KB in their models. We show how to combine the disparate representations used by these two approaches, presenting for the first time a semantic parser that (1) produces compositional, executable representations of language, (2) can successfully leverage the information contained in both a formal KB and a large corpus, and (3) is not limited to the schema of the underlying KB. We demonstrate significantly improved performance over state-of-the-art baselines on an open-domain natural language question answering task.Comment: Re-written abstract and intro, other minor changes throughout. This version published at AAAI 201