Probabilistic Relational Model Benchmark Generation

The validation of any database mining methodology goes through an evaluation process where benchmarks availability is essential. In this paper, we aim to randomly generate relational database benchmarks that allow to check probabilistic dependencies among the attributes. We are particularly interested in Probabilistic Relational Models (PRMs), which extend Bayesian Networks (BNs) to a relational data mining context and enable effective and robust reasoning over relational data. Even though a panoply of works have focused, separately , on the generation of random Bayesian networks and relational databases, no work has been identified for PRMs on that track. This paper provides an algorithmic approach for generating random PRMs from scratch to fill this gap. The proposed method allows to generate PRMs as well as synthetic relational data from a randomly generated relational schema and a random set of probabilistic dependencies. This can be of interest not only for machine learning researchers to evaluate their proposals in a common framework, but also for databases designers to evaluate the effectiveness of the components of a database management system

Probabilistic Latent Tensor Factorization Model for Link Pattern Prediction in Multi-relational Networks

This paper aims at the problem of link pattern prediction in collections of objects connected by multiple relation types, where each type may play a distinct role. While common link analysis models are limited to single-type link prediction, we attempt here to capture the correlations among different relation types and reveal the impact of various relation types on performance quality. For that, we define the overall relations between object pairs as a \textit{link pattern} which consists in interaction pattern and connection structure in the network, and then use tensor formalization to jointly model and predict the link patterns, which we refer to as \textit{Link Pattern Prediction} (LPP) problem. To address the issue, we propose a Probabilistic Latent Tensor Factorization (PLTF) model by introducing another latent factor for multiple relation types and furnish the Hierarchical Bayesian treatment of the proposed probabilistic model to avoid overfitting for solving the LPP problem. To learn the proposed model we develop an efficient Markov Chain Monte Carlo sampling method. Extensive experiments are conducted on several real world datasets and demonstrate significant improvements over several existing state-of-the-art methods.Comment: 19pages, 5 figure

Numeric Input Relations for Relational Learning with Applications to Community Structure Analysis

Most work in the area of statistical relational learning (SRL) is focussed on discrete data, even though a few approaches for hybrid SRL models have been proposed that combine numerical and discrete variables. In this paper we distinguish numerical random variables for which a probability distribution is defined by the model from numerical input variables that are only used for conditioning the distribution of discrete response variables. We show how numerical input relations can very easily be used in the Relational Bayesian Network framework, and that existing inference and learning methods need only minor adjustments to be applied in this generalized setting. The resulting framework provides natural relational extensions of classical probabilistic models for categorical data. We demonstrate the usefulness of RBN models with numeric input relations by several examples. In particular, we use the augmented RBN framework to define probabilistic models for multi-relational (social) networks in which the probability of a link between two nodes depends on numeric latent feature vectors associated with the nodes. A generic learning procedure can be used to obtain a maximum-likelihood fit of model parameters and latent feature values for a variety of models that can be expressed in the high-level RBN representation. Specifically, we propose a model that allows us to interpret learned latent feature values as community centrality degrees by which we can identify nodes that are central for one community, that are hubs between communities, or that are isolated nodes. In a multi-relational setting, the model also provides a characterization of how different relations are associated with each community

Probabilistic models for mining imbalanced relational data

Most data mining and pattern recognition techniques are designed for learning from at data files with the assumption of equal populations per class. However, most real-world data are stored as rich relational databases that generally have imbalanced class distribution. For such domains, a rich relational technique is required to accurately model the different objects and relationships in the domain, which can not be easily represented as a set of simple attributes, and at the same time handle the imbalanced class problem.Motivated by the significance of mining imbalanced relational databases that represent the majority of real-world data, learning techniques for mining imbalanced relational domains are investigated. In this thesis, the employment of probabilistic models in mining relational databases is explored. In particular, the Probabilistic Relational Models (PRMs) that were proposed as an extension of the attribute-based Bayesian Networks. The effectiveness of PRMs in mining real-world databases was explored by learning PRMs from a real-world university relational database. A visual data mining tool is also proposed to aid the interpretation of the outcomes of the PRM learned models.Despite the effectiveness of PRMs in relational learning, the performance of PRMs as predictive models is significantly hindered by the imbalanced class problem. This is due to the fact that PRMs share the assumption common to other learning techniques of relatively balanced class distributions in the training data. Therefore, this thesis proposes a number of models utilizing the effectiveness of PRMs in relational learning and extending it for mining imbalanced relational domains.The first model introduced in this thesis examines the problem of mining imbalanced relational domains for a single two-class attribute. The model is proposed by enriching the PRM learning with the ensemble learning technique. The premise behind this model is that an ensemble of models would attain better performance than a single model, as misclassification committed by one of the models can be often correctly classified by others.Based on this approach, another model is introduced to address the problem of mining multiple imbalanced attributes, in which it is important to predict several attributes rather than a single one. In this model, the ensemble bagging sampling approach is exploited to attain a single model for mining several attributes. Finally, the thesis outlines the problem of imbalanced multi-class classification and introduces a generalized framework to handle this problem for both relational and non-relational domains

Transforming Graph Representations for Statistical Relational Learning

Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical relational learning (SRL) algorithms to these domains. In this article, we examine a range of representation issues for graph-based relational data. Since the choice of relational data representation for the nodes, links, and features can dramatically affect the capabilities of SRL algorithms, we survey approaches and opportunities for relational representation transformation designed to improve the performance of these algorithms. This leads us to introduce an intuitive taxonomy for data representation transformations in relational domains that incorporates link transformation and node transformation as symmetric representation tasks. In particular, the transformation tasks for both nodes and links include (i) predicting their existence, (ii) predicting their label or type, (iii) estimating their weight or importance, and (iv) systematically constructing their relevant features. We motivate our taxonomy through detailed examples and use it to survey and compare competing approaches for each of these tasks. We also discuss general conditions for transforming links, nodes, and features. Finally, we highlight challenges that remain to be addressed