Embedding Based Link Prediction for Knowledge Graph Completion

Knowledge Graphs (KGs) are the most widely used representation of structured information about a particular domain consisting of billions of facts in the form of entities (nodes) and relations (edges) between them. Besides, the KGs also encapsulate the semantic type information of the entities. The last two decades have witnessed a constant growth of KGs in various domains such as government, scholarly data, biomedical domains, etc. KGs have been used in Machine Learning based applications such as entity linking, question answering, recommender systems, etc. Open KGs are mostly heuristically created, automatically generated from heterogeneous resources such as text, images, etc., or are human-curated. However, these KGs are often incomplete, i.e., there are missing links between the entities and missing links between the entities and their corresponding entity types. This thesis focuses on addressing these two challenges of link prediction for Knowledge Graph Completion (KGC): \textbf{(i)} General Link Prediction in KGs that include head and tail prediction, triple classification, and \textbf{(ii)} Entity Type Prediction. Most of the graph mining algorithms are proven to be of high complexity, deterring their usage in KG-based applications. In recent years, KG embeddings have been trained to represent the entities and relations in the KG in a low-dimensional vector space preserving the graph structure. In most published works such as the translational models, convolutional models, semantic matching, etc., the triple information is used to generate the latent representation of the entities and relations. In this dissertation, it is argued that contextual information about the entities obtained from the random walks, and textual entity descriptions, are the keys to improving the latent representation of the entities for KGC. The experimental results show that the knowledge obtained from the context of the entities supports the hypothesis. Several methods have been proposed for KGC and their effectiveness is shown empirically in this thesis. Firstly, a novel multi-hop attentive KG embedding model MADLINK is proposed for Link Prediction. It considers the contextual information of the entities by using random walks as well as textual entity descriptions of the entities. Secondly, a novel architecture exploiting the information contained in a pre-trained contextual Neural Language Model (NLM) is proposed for Triple Classification. Thirdly, the limitations of the current state-of-the-art (SoTA) entity type prediction models have been analysed and a novel entity typing model CAT2Type is proposed that exploits the Wikipedia Categories which is one of the most under-treated features of the KGs. This model can also be used to predict missing types of unseen entities i.e., the newly added entities in the KG. Finally, another novel architecture GRAND is proposed to predict the missing entity types in KGs using multi-label, multi-class, and hierarchical classification by leveraging different strategic graph walks in the KGs. The extensive experiments and ablation studies show that all the proposed models outperform the current SoTA models and set new baselines for KGC. The proposed models establish that the NLMs and the contextual information of the entities in the KGs together with the different neural network architectures benefit KGC. The promising results and observations open up interesting scopes for future research involving exploiting the proposed models in domain-specific KGs such as scholarly data, biomedical data, etc. Furthermore, the link prediction model can be exploited as a base model for the entity alignment task as it considers the neighbourhood information of the entities

Testing for Differences in Gaussian Graphical Models: Applications to Brain Connectivity

Functional brain networks are well described and estimated from data with Gaussian Graphical Models (GGMs), e.g. using sparse inverse covariance estimators. Comparing functional connectivity of subjects in two populations calls for comparing these estimated GGMs. Our goal is to identify differences in GGMs known to have similar structure. We characterize the uncertainty of differences with confidence intervals obtained using a parametric distribution on parameters of a sparse estimator. Sparse penalties enable statistical guarantees and interpretable models even in high-dimensional and low-sample settings. Characterizing the distributions of sparse models is inherently challenging as the penalties produce a biased estimator. Recent work invokes the sparsity assumptions to effectively remove the bias from a sparse estimator such as the lasso. These distributions can be used to give confidence intervals on edges in GGMs, and by extension their differences. However, in the case of comparing GGMs, these estimators do not make use of any assumed joint structure among the GGMs. Inspired by priors from brain functional connectivity we derive the distribution of parameter differences under a joint penalty when parameters are known to be sparse in the difference. This leads us to introduce the debiased multi-task fused lasso, whose distribution can be characterized in an efficient manner. We then show how the debiased lasso and multi-task fused lasso can be used to obtain confidence intervals on edge differences in GGMs. We validate the techniques proposed on a set of synthetic examples as well as neuro-imaging dataset created for the study of autism

Soft behaviour modelling of user communities

A soft modelling approach for describing behaviour in on-line user communities is introduced in this work. Behaviour models of individual users in dynamic virtual environments have been described in the literature in terms of timed transition automata; they have various drawbacks. Soft multi/agent behaviour automata are defined and proposed to describe multiple user behaviours and to recognise larger classes of user group histories, such as group histories which contain unexpected behaviours. The notion of deviation from the user community model allows defining a soft parsing process which assesses and evaluates the dynamic behaviour of a group of users interacting in virtual environments, such as e-learning and e-business platforms. The soft automaton model can describe virtually infinite sequences of actions due to multiple users and subject to temporal constraints. Soft measures assess a form of distance of observed behaviours by evaluating the amount of temporal deviation, additional or omitted actions contained in an observed history as well as actions performed by unexpected users. The proposed model allows the soft recognition of user group histories also when the observed actions only partially meet the given behaviour model constraints. This approach is more realistic for real-time user community support systems, concerning standard boolean model recognition, when more than one user model is potentially available, and the extent of deviation from community behaviour models can be used as a guide to generate the system support by anticipation, projection and other known techniques. Experiments based on logs from an e-learning platform and plan compilation of the soft multi-agent behaviour automaton show the expressiveness of the proposed model

Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces

Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.Comment: 32 pages, 6 figure

Asymptotic theory for Bayesian inference and prediction: from the ordinary to a conditional Peaks-Over-Threshold method

The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT method there is no asymptotic theory for such proposals. Even more importantly, the ambitious and challenging problem of predicting future extreme events according to a proper probabilistic forecasting approach has received no attention to date. In this paper we develop the asymptotic theory (consistency, contraction rates, asymptotic normality and asymptotic coverage of credible intervals) for the Bayesian inference based on the POT method. We extend such an asymptotic theory to cover the Bayesian inference on the tail properties of the conditional distribution of a response random variable conditionally to a vector of random covariates. With the aim to make accurate predictions of severer extreme events than those occurred in the past, we specify the posterior predictive distribution of a future unobservable excess variable in the unconditional and conditional approach and we prove that is Wasserstein consistent and derive its contraction rates. Simulations show the good performances of the proposed Bayesian inferential methods. The analysis of the change in the frequency of financial crises over time shows the utility of our methodology