Luis M. de Campos

Serafin Moral, Luis M. de Campos

This paper presents a procedure to determine a complete belief function from the known values of belief for some of the subsets of the frame of discerment. The method is based on the principle of minimum commitment and a new principle called the focusing principle. This additional principle is based on the idea that belief is specified for the most relevant sets: the focal elements. The resulting procedure is compared with existing methods of building complete belief functions: the minimum specificity principle and the least commitment principle.

Luis M. de Campos, Serafin Moral

In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independence. The first is irrelevance. Two variables are independent when a change on the knowledge about one variable does not affect the other. The second one is factorization. Two variables are independent when the joint convex set of probabilities can be decomposed on the product of marginal convex sets. In the case of the Theory of Probability, these two starting points give rise to the same definition. In the case of convex sets of probabilities, the resulting concepts will be strongly related, but they will not be equivalent. As application of the concept of independence, we shall consider the problem of building a global convex set from marginal convex sets of probabilities.

Silvia Acid, Luis M. de Campos

The criterion commonly used in directed acyclic graphs (dags) for testing graphical independence is the well-known d-separation criterion. It allows us to build graphical representations of dependency models (usually probabilistic dependency models) in the form of belief networks, which make easy interpretation and management of independence relationships possible, without reference to numerical parameters (conditional probabilities). In this paper, we study the following combinatorial problem: finding the minimum d-separating set for two nodes in a dag. This set would represent the minimum information (in the sense of minimum number of variables) necessary to prevent these two nodes from influencing each other. The solution to this basic problem and some of its extensions can be useful in several ways, as we shall see later. Our solution is based on a two-step process: first, we reduce the original problem to the simpler one of finding a minimum separating set in an undirected graph, and second, we develop an algorithm for solving it.

Luis M. de Campos, Juan F. Huete

Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two characterizations of decomposable models in terms of independence relationships, we develop an exact algorithm for recovering the chordal graphical representation of any given decomposable model. We also propose an algorithm for learning chordal approximations of dependency models isomorphic to general undirected graphs.

Luis M. de Campos, Juan M. Fernandez-Luna, Juan F. Huete

Information Retrieval (IR) is concerned with the identification of documents in a collection that are relevant to a given information need, usually represented as a query containing terms or keywords, which are supposed to be a good description of what the user is looking for. IR systems may improve their effectiveness (i.e., increasing the number of relevant documents retrieved) by using a process of query expansion, which automatically adds new terms to the original query posed by an user. In this paper we develop a method of query expansion based on Bayesian networks. Using a learning algorithm, we construct a Bayesian network that represents some of the relationships among the terms appearing in a given document collection; this network is then used as a thesaurus (specific for that collection). We also report the results obtained by our method on three standard test collections.

Alfonso E. Romero, Luis M. de Campos

Multilabel classification is a relatively recent subfield of machine learning. Unlike to the classical approach, where instances are labeled with only one category, in multilabel classification, an arbitrary number of categories is chosen to label an instance. Due to the problem complexity (the solution is one among an exponential number of alternatives), a very common solution (the binary method) is frequently used, learning a binary classifier for every category, and combining them all afterwards. The assumption taken in this solution is not realistic, and in this work we give examples where the decisions for all the labels are not taken independently, and thus, a supervised approach should learn those existing relationships among categories to make a better classification. Therefore, we show here a generic methodology that can improve the results obtained by a set of independent probabilistic binary classifiers, by using a combination procedure with a classifier trained on the co-occurrences of the labels. We show an exhaustive experimentation in three different standard corpora of labeled documents (Reuters-21578, Ohsumed-23 and RCV1), which present noticeable improvements in all of them, when using our methodology, in three probabilistic base classifiers.