Serafín Moral

Symbolic and Quantitative Approaches to Reasoning with Uncertainty

In recent years it has become apparent that an important part of the theory of artificial intelligence is concerned with reasoning on the basis of uncertain, incomplete, or inconsistent information. A variety of formalisms have been developed, including nonmonotonic logic, fuzzy sets, possibility theory, belief functions, and dynamic models of reasoning such as belief revision and Bayesian networks. Several European research projects have been formed in the area and the first European conference was held in 1991. This volume contains the papers accepted for presentation at ECSQARU-93, the European Conference on Symbolicand Quantitative Approaches to Reasoning and Uncertainty, held at the University of Granada, Spain, November 8-10, 1993.

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.

Mixtures of Truncated Exponentials in Hybrid Bayesian Networks

In this paper we propose the use of mixtures of truncated exponential (MTE) distributions in hybrid Bayesian networks. We study the properties of the MTE distribution and show how exact probability propagation can be carried out by means of a local computation algorithm. One feature of this model is that no restriction is made about the order among the variables either discrete or continuous. Computations are performed over a representation of probabilistic potentials based on probability trees, expanded to allow discrete and continuous variables simultaneously. Finally, a Markov chain Monte Carlo algorithm is described with the aim of dealing with complex networks.

A survey of concepts of independence for imprecise probabilities

Our aim in this paper is to clarify the notion of independence for imprecise probabilities. Suppose that two marginal experiments are each described by an imprecise probability model, i.e., by a convex set of probability distributions or an equivalent model such as upper and lower probabilities or previsions. Then there are several ways to define independence of the two experiments and to construct an imprecise probability model for the joint experiment. We survey and compare six definitions of independence. To clarify the meaning of the definitions and the relationships between them, we give simple examples which involve drawing balls from urns. For each concept of independence, we give a mathematical definition, an intuitive or behavioural interpretation, assumptions under which the definition is justified, and an example of an urn model to which the definition is applicable. Each of the independence concepts we study appears to be useful in some kinds of application. The concepts of strong independence and epistemic independence appear to be the most frequently applicable.

Fusion: General concepts and characteristics

The problem of combining pieces of information issued from several sources can be encountered in various fields of application. This paper aims at presenting the different aspects of information fusion in different domains, such as databases, regulations, preferences, sensor fusion, etc., at a quite general level. We first present different types of information encountered in fusion problems, and different aims of the fusion process. Then we focus on representation issues which are relevant when discussing fusion problems. An important issue is then addressed, the handling of conflicting information. We briefly review different domains where fusion is involved, and describe how the fusion problems are stated in each domain. Since the term fusion can have different, more or less broad, meanings, we specify later some terminology with respect to related problems, that might be included in a broad meaning of fusion. Finally we briefly discuss the difficult aspects of validation and evaluation. © 2001 John Wiley & Sons, Inc.

On the concept of possibility-probability consistency

Both probability and possibility may be seen as information about an experiment. It is conceivable to have at some time these two forms of information about a same experiment and then the question of the relation between them arises at once. In this paper some aspects of the concept of possibility-probability consistency are studied. The consistency is considered as a fuzzy property relative to the coherence between possibilistic and probabilistic information. We analyse several measures of the degree of consistency and introduce an axiomatic to characterize them.

Importance sampling in Bayesian networks using probability trees

In this paper a new Monte-Carlo algorithm for the propagation of probabilities in Bayesian networks is proposed. This algorithm has two stages: in the first one an approximate propagation is carried out by means of a deletion sequence of the variables. In the second stage a sample is obtained using as sampling distribution the calculations of the first step. The different configurations of the sample are weighted according to the importance sampling technique. We show how the use of probability trees to store and to approximate probability potentials, and a careful selection of the deletion sequence, make this algorithm able to propagate over large networks with extreme probabilities.

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.

Building classification trees using the total uncertainty criterion

We present an application of the measure of total uncertainty on convex sets of probability distributions, also called credal sets, to the construction of classification trees. In these classification trees the probabilities of the classes in each one of its leaves is estimated by using the imprecise Dirichlet model. In this way, smaller samples give rise to wider probability intervals. Branching a classification tree can decrease the entropy associated with the classes but, at the same time, as the sample is divided among the branches the nonspecificity increases. We use a total uncertainty measure (entropy + nonspecificity) as branching criterion. The stopping rule is not to increase the total uncertainty. The good behavior of this procedure for the standard classification problems is shown. It is important to remark that it does not experience of overfitting, with similar results in the training and test samples.

Using probability trees to compute marginals with imprecise probabilities

This paper presents an approximate algorithm to obtain a posteriori intervals of probability, when available information is also given with intervals. The algorithm uses probability trees as a means of representing and computing with the convex sets of probabilities associated to the intervals.