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The need to deal with the inherent uncertainty in real-world relational or networked data leads to the proposal of new probabilistic models, such as probabilistic graphs. Every edge in a probabilistic graph is associated with a probability whose value represents the likelihood of its existence, or the strength of the relation between the entities it connects. The aim of this paper is to propose two machine learning techniques for the link classification problem in relational data exploiting the probabilistic graph representation. Both the proposed methods will exploit a language-constrained reachability method to infer the probability of possible hidden relationships that may exists between two nodes in a probabilistic graph. Each hidden relationships between two nodes may be viewed as a feature (or a factor), and its corresponding probability as its weight, while an observed relationship is considered as a positive instance for its corresponding link label. Given a training set of observed links, the first learning approach is to use a propositionalization technique adopting a L2-regularized Logistic Regression to learn a model able to predict unobserved link labels. Since in some cases the edges’ probability may be not known in advance or they could not be precisely defined for a classification task, the second xposed approach is to exploit the inference method and to use a mean squared technique to learn the edges’ probabilities. Both the proposed methods have been evaluated on real world data sets and the corresponding results proved their validity.

Feature selection methods often improve the performance of attribute-value learning. We explore whether also in relational learning, examples in the form of clauses can be reduced in size to speed up learning without affecting the learned hypothesis. To this end, we introduce the notion of safe reduction: a safely reduced example cannot be distinguished from the original example under the given hypothesis language bias. Next, we consider the particular, rather permissive bias of bounded treewidth clauses. We show that under this hypothesis bias, examples of arbitrary treewidth can be reduced efficiently. We evaluate our approach on four data sets with the popular system Aleph and the state-of-the-art relational learner nFOIL. On all four data sets we make learning faster in the case of nFOIL, achieving an order-of-magnitude speed up on one of the data sets, and more accurate in the case of Aleph.

Attribute-value based representations, standard in today's data mining systems, have a limited expressiveness. Inductive Logic Programming provides an interesting alternative, particularly for learning from structured examples whose parts, each with its own attributes, are related to each other by means of first-order predicates. Several subsets of first-order logic (FOL) with different expressive power have been proposed in Inductive Logic Programming (ILP). The challenge lies in the fact that the more expressive the subset of FOL the learner works with, the more critical the dimensionality of the learning task. The Datalog language is expressive enough to represent realistic learning problems when data is given directly in a relational database, making it a suitable tool for data mining. Consequently, it is important to elaborate techniques that will dynamically decrease the dimensionality of learning tasks expressed in Datalog, just as Feature Subset Selection (FSS) techniques do it in attribute-value learning. The idea of re-using these techniques in ILP runs immediately into a problem as ILP examples have variable size and do not share the same set of literals. We propose here the first paradigm that brings Feature Subset Selection to the level of ILP, in languages at least as expressive as Datalog. The main idea is to first perform a change of representation, which approximates the original relational problem by a multi-instance problem. The representation obtained as the result is suitable for FSS techniques which we adapted from attribute-value learning by taking into account some of the characteristics of the data due to the change of representation. We present the simple FSS proposed for the task, the requisite change of representation, and the entire method combining those two algorithms. The method acts as a filter, preprocessing the relational data, prior to the model building, which outputs relational examples with empirically relevant literals. We discuss experiments in which the method was successfully applied to two real-world domains.

This paper demonstrates the relational structure of belief networks by establishing an extended relational data model which can be applied to both belief networks and relational applications. It is demonstrated that a Markov network can be represented as a generalized acyclic join dependency (GAJD) which is equivalent to a set of conflict-free generalized multivalued dependencies (GMVDs). A Markov network can also be characterized by an entropy function, which greatly facilitates the manipulation of GMVDs. These results are extensions of results established in relational theory. It is shown that there exists a complete set of inference rules for the GMVDs. This result is important from a probabilistic perspective. All the above results explicitly demonstrate that there is a unified model for relational database and probabilistic reasoning systems. This is not only important from a theoretical point of view in that one model has been developed for a number of domains, but also from a practical point of view in that one system can be implemented for both domains. This implemented system can take advantage of the performance enhancing techniques developed in both fields. Thereby, this paper serves as a theoretical foundation for harmonizing these two important information domains.

Probabilistic methods provide a formalism for reasoning about partial beliefs under conditions of uncertainty. This paper suggests a new representation of probabilistic knowledge. This representation encompasses the traditional relational database model. In particular, it is shown that probabilistic conditional independence is equivalent to the notion of generalized multivalued dependency. More importantly, a Markov network can be viewed as a generalized acyclic join dependency. This linkage between these two apparently different but closely related knowledge representations provides a foundation for developing a unified model for probabilistic reasoning and relational database systems.

We propose a novel framework for generating classification rules from relational data. This is a specialized version of the general framework intended for mining relational data and is defined in granular computing theory. In the framework proposed in this paper we define a method for deriving information granules from relational data. Such granules are the basis for generating relational classification rules. In our approach we follow the granular computing idea of switching between different levels of granularity of the universe. Thanks to this a granule-based relational data representation can easily be replaced by another one and thereby adjusted to a given data mining task, e.g. classification. A generalized relational data representation, as defined in the framework, can be treated as the search space for generating rules. On account of this the size of the search space may significantly be limited. Furthermore, our framework, unlike others, unifies not only the way the data and rules to be derived are expressed and specified, but also partially the process of generating rules from the data. Namely, the rules can be directly obtained from the information granules or constructed based on them.