Abstract de nuestro grupo en 1997/UTAI Research Group Abstracts in 1997

Removing partial inconsistency in Valuation-Based Systems
BY Luis M. de Campos, Serafín Moral

International Journal of Intelligent Systems 12, 629--653, 1997.

This paper presents an abstract definition of partial inconsistency and one operator used to remove it: normalization. When there is partial inconsistency in the combination of two pieces of information, this partial inconsistency is propagated to all the information in the system thereby degrading it. To avoid this effect, it is necessary to apply normalization. Four different formalisms are studied as particular cases of the axiomatic framework presented in this paper: probability theory, infinitesimal probabilities, possibility theory, and symbolic evidence theory. It is shown how, in one of these theories (probability), normalization is not an important problem: a property which is verified in this case gives rise to the equivalence of all the different normalization strategies. Things are very different for the other three theories: there are a number of different normalization procedures. The main objective of this paper will be to determine conditions based on general principles indicating how and when the normalization operator should be applied.

Mixing Exact and Importance Sampling Propagation Algorithms in Dependence Graphs
BY Luis D. Hernández, Serafín Moral

International Journal of Intelligent Systems 12, 553--576, 1997.

In this paper a new algorithm is presented for the propagation of probabilities in junction trees. It is based on a hybrid methodology. Given a junction tree, some of the nodes carry out an exact calculation, and the other an approximation by Monte-Carlo methods. For the exact calculation we will use Shafer/Shenoy method and for the Monte-Carlo estimation a general class of importance sampling algorithms is used. We briefly study how to apply this sampler on the clusters in a junction tree. The basic algorithm and some of its variations are presented, depending on the family of functions to which we apply the importance sampler: potentials or/and messages in the tree. An experimental evaluation is carried out, comparing their performance with the well known likelihood weighting approximated algorithm. This family of methods shows a very promising performance.

On the Use of Independence Relationships for Learning Simplified Belief Networks
BY Luis M. de Campos, Juan F. Huete

International Journal of Intelligent Systems 12, 495-522 (1997), 1997. (28 pages)

Belief networks are graphic structures capable of representing dependence and independence relationships among variables in a given domain of knowledge. We focus on the problem of automatic learning of these structures from data, and restrict our study to a specific type of belief network: simple graphs, i.e., directed acyclic graphs where every pair of nodes with a common direct child has no common ancestor nor is one an ancestor of the other. Our study is based on an analysis of the independence relationships that may be represented by means of simple graphs. This theoretical study, which includes new characterizations of simple graphs in terms of independence relationships, is the basis of an efficient algorithm that recovers simple graphs using only zero and first-order conditional independence tests, thereby overcoming some of the practical difficulties of existing algorithms.

Aggregation of imprecise probabilities
BY S. Moral, J. del Sagrado

In: Aggregation and Fusion of Imperfect Information (B. Bouchon-Meunier, ed.) Physica Verlag, Heidelberg, 162-188, 1987.

Methods to aggregate convex sets of probabilities are proposed. Source reliability is taken into account by transforming the given information and making it less precise. An important property of the aggregation will be that the precision of the result will depend on the initial compatibility of sources. Special attention will be paid to the particular case of probability intervals giving adaptations of aggregation procedures.

Propagación Exacta y Aproximada Mediante Arboles de Probabilidad en Redes Causales
BY A. Cano and S. Moral

Actas de la VII conferencia de la Asociación Española Para la Inteligencia Artificial (CAEPIA'97) 635-644, 1997.

Recientemente han sido propuestos diferentes métodos para aprovechar las independencias asimétricas de una red causal en una inferencia más eficiente. Uno de estos métodos hace uso de árboles de probabilidad. En este trabajo se propone trabajar directamente con los árboles de probabilidad asociados a cada potencial describiendo cómo se pueden implementar los algoritmos de propagación en estructuras gráficas usando árboles en lugar de matrices para representar las probabilidades condicionadas. Esto permite además el diseño de algoritmos aproximados, en los que el tamaño de un potencial tiene un límite fijado de antemano.

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