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 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

Induction of Interpretable Possibilistic Logic Theories from Relational Data

The field of Statistical Relational Learning (SRL) is concerned with learning probabilistic models from relational data. Learned SRL models are typically represented using some kind of weighted logical formulas, which make them considerably more interpretable than those obtained by e.g. neural networks. In practice, however, these models are often still difficult to interpret correctly, as they can contain many formulas that interact in non-trivial ways and weights do not always have an intuitive meaning. To address this, we propose a new SRL method which uses possibilistic logic to encode relational models. Learned models are then essentially stratified classical theories, which explicitly encode what can be derived with a given level of certainty. Compared to Markov Logic Networks (MLNs), our method is faster and produces considerably more interpretable models.Comment: Longer version of a paper appearing in IJCAI 201

Learning Tuple Probabilities

Learning the parameters of complex probabilistic-relational models from labeled training data is a standard technique in machine learning, which has been intensively studied in the subfield of Statistical Relational Learning (SRL), but---so far---this is still an under-investigated topic in the context of Probabilistic Databases (PDBs). In this paper, we focus on learning the probability values of base tuples in a PDB from labeled lineage formulas. The resulting learning problem can be viewed as the inverse problem to confidence computations in PDBs: given a set of labeled query answers, learn the probability values of the base tuples, such that the marginal probabilities of the query answers again yield in the assigned probability labels. We analyze the learning problem from a theoretical perspective, cast it into an optimization problem, and provide an algorithm based on stochastic gradient descent. Finally, we conclude by an experimental evaluation on three real-world and one synthetic dataset, thus comparing our approach to various techniques from SRL, reasoning in information extraction, and optimization

A Simple Relational Classifier

We analyze a Relational Neighbor (RN) classifier, a simple relational predictive model that predicts only based on class labels of related neighbors, using no learning and no inherent attributes.We show that it performs surprisingly well by comparing it to more complex models such as Probabilistic Relational Models and Relational Probability Trees on three data sets from published work. We argue that a simple model such as this should be used as a baseline to assess the performance of relational learners.NYU, Stern School of Business, IOMS department, Center for Digital Economy Researc

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