Luis M. de Campos

PROBABILITY INTERVALS: A TOOL FOR UNCERTAIN REASONING

We study probability intervals as an interesting tool to represent uncertain information. A number of basic operations necessary to develop a calculus with probability intervals, such as combination, marginalization, conditioning and integration are studied in detail. Moreover, probability intervals are compared with other uncertainty theories, such as lower and upper probabilities, Choquet capacities of order two and belief and plausibility functions. The advantages of probability intervals with respect to these formalisms in computational efficiency are also highlighted.

Ant colony optimization for learning Bayesian networks

One important approach to learning Bayesian networks (BNs) from data uses a scoring metric to evaluate the fitness of any given candidate network for the data base, and applies a search procedure to explore the set of candidate networks. The most usual search methods are greedy hill climbing, either deterministic or stochastic, although other techniques have also been used. In this paper we propose a new algorithm for learning BNs based on a recently introduced metaheuristic, which has been successfully applied to solve a variety of combinatorial optimization problems: ant colony optimization (ACO). We describe all the elements necessary to tackle our learning problem using this metaheuristic, and experimentally compare the performance of our ACO-based algorithm with other algorithms used in the literature. The experimental work is carried out using three different domains: ALARM, INSURANCE and BOBLO.

Combining content-based and collaborative recommendations: A hybrid approach based on Bayesian networks

Recommender systems enable users to access products or articles that they would otherwise not be aware of due to the wealth of information to be found on the Internet. The two traditional recommendation techniques are content-based and collaborative filtering. While both methods have their advantages, they also have certain disadvantages, some of which can be solved by combining both techniques to improve the quality of the recommendation. The resulting system is known as a hybrid recommender system. In the context of artificial intelligence, Bayesian networks have been widely and successfully applied to problems with a high level of uncertainty. The field of recommendation represents a very interesting testing ground to put these probabilistic tools into practice. This paper therefore presents a new Bayesian network model to deal with the problem of hybrid recommendation by combining content-based and collaborative features. It has been tailored to the problem in hand and is equipped with a flexible topology and efficient mechanisms to estimate the required probability distributions so that probabilistic inference may be performed. The effectiveness of the model is demonstrated using the MovieLens and IMDB data sets.

A new approach for learning belief networks using independence criteria

In the paper we describe a new independence-based approach for learning Belief Networks. The proposed algorithm avoids some of the drawbacks of this approach by making an intensive use of low order conditional independence tests. Particularly, the set of zero- and first-order independence statements are used in order to obtain a prior skeleton of the network, and also to fix and remove arrows from this skeleton. Then, a refinement procedure, based on minimum cardinality d-separating sets, which uses a small number of conditional independence tests of higher order, is carried out to produce the final graph. Our algorithm needs an ordering of the variables in the model as the input. An algorithm that partially overcomes this problem is also presented. ” 2000

Characterization and comparison of Sugeno and Choquet integrals

Abstract Starting from the concept of ‘equiordered functions’ we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure: Sugeno and Choquet integrals. The characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals, pointing out their formal similarities and their conceptual differences.

Searching for Bayesian network structures in the space of restricted acyclic partially directed graphs

Although many algorithms have been designed to construct Bayesian network structures using different approaches and principles, they all employ only two methods: those based on independence criteria, and those based on a scoring function and a search procedure (although some methods combine the two). Within the score+search paradigm, the dominant approach uses local search methods in the space of directed acyclic graphs (DAGs), where the usual choices for defining the elementary modifications (local changes) that can be applied are arc addition, arc deletion, and arc reversal. In this paper, we propose a new local search method that uses a different search space, and which takes account of the concept of equivalence between network structures: restricted acyclic partially directed graphs (RPDAGs). In this way, the number of different configurations of the search space is reduced, thus improving efficiency. Moreover, although the final result must necessarily be a local optimum given the nature of the search method, the topology of the new search space, which avoids making early decisions about the directions of the arcs, may help to find better local optima than those obtained by searching in the DAG space. Detailed results of the evaluation of the proposed search method on several test problems, including the well-known Alarm Monitoring System, are also presented.

The concept of conditional fuzzy measure

In this article a concept of conditional fuzzy measure is presented, which is a generalization of conditional probability measure. Its properties are studied in the general case and in some particular types of fuzzy measures as representable measures, capacities of order two, and belief‐plausibility measures. In the case of capacities of order two it coincides with the concept given by Dempster for representable measures. However, it differs from the Dempsters rule for conditioning belief‐plausibility measures. As it is shown, Dempsters rule of conditioning is based on the idea of combining information and our definition is based on a restriction in the set of possible worlds.

Bayesian network learning algorithms using structural restrictions

The use of several types of structural restrictions within algorithms for learning Bayesian networks is considered. These restrictions may codify expert knowledge in a given domain, in such a way that a Bayesian network representing this domain should satisfy them. The main goal of this paper is to study whether the algorithms for automatically learning the structure of a Bayesian network from data can obtain better results by using this prior knowledge. Three types of restrictions are formally defined: existence of arcs and/or edges, absence of arcs and/or edges, and ordering restrictions. We analyze the possible interactions between these types of restrictions and also how the restrictions can be managed within Bayesian network learning algorithms based on both the score+search and conditional independence paradigms. Then we particularize our study to two classical learning algorithms: a local search algorithm guided by a scoring function, with the operators of arc addition, arc removal and arc reversal, and the PC algorithm. We also carry out experiments using these two algorithms on several data sets.

A comparison of learning algorithms for Bayesian networks: a case study based on data from an emergency medical service

Due to the uncertainty of many of the factors that influence the performance of an emergency medical service, we propose using Bayesian networks to model this kind of system. We use different algorithms for learning Bayesian networks in order to build several models, from the hospital managers point of view, and apply them to the specific case of the emergency service of a Spanish hospital. This first study of a real problem includes preliminary data processing, the experiments carried out, the comparison of the algorithms from different perspectives, and some potential uses of Bayesian networks for management problems in the health service.

Independence concepts in possibility theory: part I

Abstract From both a theoretical and a practical point of view, the study of the concept of independence has great importance in any formalism that manages uncertainty. In Independence Concepts in Possibility Theory: Part I (de Campos and Huete, Fuzzy Sets and Systems 103 (1999) 127–152) several independence relationships were proposed, using different comparison criteria between conditional possibility measures, and using Hisdal conditioning as the conditioning operator. In this paper, we follow the same approach, but considering possibility measures as particular cases of consonant plausibility measures and, therefore, using Dempster conditioning instead of Hisdals. We formalize several intuitive ideas to define independence relationships, namely ‘not to modify’, ‘not to gain’ and ‘to obtain similar’ information after conditioning, and study their properties. We also compare the results with the previous ones obtained in Part I using Hisdal conditioning. Finally, the marginal problem, i.e., how to obtain a joint possibility distribution from a set of marginals, and the problem of factorizing large possibility distributions, in terms of its conditionally independent components, are considered.