de ses descendants, aussi dit descendance, ou lignée descendante, de i qui s'obtient par itération de la relation " ? etre enfant " : d(i) = {j ; ?(l 0 , . . . , l k ) l 0 = i , l k = j , ? s ? {1, p.1 ,
racine " et " feuille " sont plutôt réservés au cas des arborescences ; dans le cas des graphes orientés les plus généraux, les termes correspondants seraient alors " source " et " puits ,
n} p(i s ) ? {i 1 ,
Il résulte immédiatement de la définition que : 1. ? s ? {1, . . . , n} ?(i s ) ? {i 1 , . . . , i s?1 }, c'estàestà dire que toutélémenttoutélément est classé après tous ceux de sa lignée ,
n} d(i s ) ? {i 1 , . . . , i s?1 } = ?, c'estàestà dire qu'avant unélémentunélément donné n'est classé aucun de ses descendants ,
The generalized distributive law, IEEE Trans. Inform. Theory, vol.46, issue.1, pp.325-343, 2000. ,
Les Réseaux Bayésiens, 1999. ,
Graphs and Hypergraphs, 1973. ,
Expert Systems and Probabilistic Network Models, Monographs in Computer Science, 1997. ,
DOI : 10.1007/978-1-4612-2270-5
Inference in belief networks : A procedural guide, International Journal of Approximate Reasoning, vol.15, pp.225-263, 1996. ,
Bayesian networks without tears : making bayesian networks more accessible to the probabilistically unsophisticated, AI Mag, vol.12, issue.4, pp.50-63, 1991. ,
The computational complexity of probabilistic inference using bayesian belief networks, Artificial Intelligence, vol.42, issue.2-3, pp.393-405, 1990. ,
DOI : 10.1016/0004-3702(90)90060-D
Determination of the entropy of a belief network is np-hard, 1991. ,
A diagnostic method that uses casual knowledge and linear programming in the application of bayes' formula, Computer Methods and Programs in Biomedicine, 1986. ,
Probabilistic inference using belief networks is np-hard, pp.393-405, 1987. ,
Computer-Based Medical Diagnosis Using Belief Networks and Bounded Probabilities, Selected Topics in Medical Artificial Intelligence, pp.85-97, 1988. ,
DOI : 10.1007/978-1-4613-8777-0_7
Expert systems based on belief networks, Current Research Directions, 1988. ,
Advanced Inference in Bayesian Networks, Statistics, vol.19, pp.301-312, 2000. ,
DOI : 10.1007/978-94-011-5014-9_2
Bucket Elimination: A Unifying Framework for Probabilistic Inference, Proc. Twelthth Conf. on Uncertainty in Artificial Intelligence, pp.211-219, 1996. ,
DOI : 10.1007/978-94-011-5014-9_4
An introduction to Bayesian Networks [17] Corset Franck. Aidè a l'optimisation de maintenancè a partir de réseaux bayésiens et fiabilité dans un contexte doublement censuré, Thèse soutenue au sein d'IS2, 1999. ,
Parameter priors for directed acyclic graphical models and the characterization of several probability distributions. The Annals of Statistics, pp.1412-1440, 2002. ,
Stratified exponential families : Graphical models and model selection, The Annals of Statistics, vol.29, pp.505-526, 2001. ,
Graphical models and variational methods ,
Graphes et algorithmes. Collection de la direction desétudes desétudes et recherches d'´ electricité de France, 1974. ,
Information Processing in Expert Systems, 1992. ,
A tractable inference algorithm for diagnosing multiple diseases, 1989. ,
A tutorial on learning with bayesian networks, Learning in Graphical Models, 1999. ,
Causal independence for probability assessment and inference using Bayesian networks, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, vol.26, issue.6, pp.826-831, 1996. ,
DOI : 10.1109/3468.541341
Bayesian networks, Communications of the ACM, vol.38, issue.3, pp.27-30, 1995. ,
DOI : 10.1145/203330.203336
The lumiere project : Bayesian user modeling for inferring the goals and needs of software users, Proceedings of Fourteenth Conference on Uncertainty in Artificial Intelligence, pp.256-265, 1998. ,
Variational methods for inference and estimation in graphical models, 1997. ,
Variational probabilistic inference and the qmr-dt database, Journal of Artificial Intelligence Research, vol.10, pp.291-322, 1998. ,
Algorithme des restrictions successives. 5` eme Congrès International Pluridisciplinaire Qualité et Sûreté de Fonctionnement, 2003. ,
Probabilistic Networks, Defeasible Reasoning and Uncertainty management Systems, pp.289-320, 2000. ,
DOI : 10.1007/978-94-017-1737-3_7
An introduction to variational methods for graphical models, Proceedings of the NATO Advanced Study Institute on Learning in graphical models, pp.105-161, 1998. ,
Bayesian networks : a model of self-activated memory for evidential reasoning, Cognitive Science Society, pp.329-334, 1985. ,
A constraint-propagation approach to probabilistic reasoning, Uncertainty in Artificial Intelligence, pp.3718-1986, 1986. ,
Fusion, propagation and structuring in belief networks, UCLA Computer Science Department Technical Report Artificial Intelligence, vol.850022, issue.29, pp.241-288, 1986. ,
Graphoids : a graph-based logic for reasoning about relevance relations, Advances in Artificial Intelligence-II, 1987. ,
Influence diagrams and d-separation, 1988. ,
Object oriented bayesian networks, Proceeding of the Thirteenth Annual Conference on Uncertainty in Artificial Intelligence, 1997. ,
Local computation with probabilities on graphical structures and their application to expert systems, Proceedings of the Royal Statistical Society, Series B, vol.50, issue.2, 1988. ,
Propagation of Probabilities, Means, and Variances in Mixed Graphical Association Models, Journal of the American Statistical Association, vol.4, issue.420, pp.1098-1108, 1992. ,
DOI : 10.1214/aos/1176347003
Graphical Models, 1996. ,
Introduction to Monte Carlo Methods, Learning in Graphical Models, NATO Science Series, pp.175-204, 1998. ,
DOI : 10.1007/978-94-011-5014-9_7
Lazy propagation in junction trees, Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence, pp.362-369, 1998. ,
An experimental comparison of several clustering and initialization methods, Machine Learning, pp.9-29, 2001. ,
Probabilistic diagnosis using a reformulation of the internist-1/qmr knowledge base ii. evaluation of diagnostic performance, Methods Inf Med, vol.30, pp.256-267, 1991. ,
Probabilistic inference using markov chain monte carlo methods, 1993. ,
Probabilistic Reasoning in Expert Systems, 1990. ,
Introduction to inference for bayesian networks, Statistics, vol.19, pp.301-312, 2000. ,
Axioms for probability and belief-function propagation, Uncertainty in Artificial Intelligence, vol.4, pp.169-198, 1990. ,
The efficient propagation of arbitrary subsets of beliefs in discretevalued bayesian belief networks, Statistics, vol.19, pp.301-312, 2000. ,
Probabilistic Independence Networks for Hidden Markov Probability Models, Neural Computation, vol.1994, issue.2, pp.227-269, 1997. ,
DOI : 10.1016/0262-8856(94)90010-8
Bayesian Analysis in Expert Systems, Statistical Science, vol.8, issue.3, pp.219-1247, 1993. ,
DOI : 10.1214/ss/1177010888
Statistical reasoning and learning in knowledge-bases represented as causal networks, Lecture Notes in Medical Informatics, vol.36, pp.105-112, 1988. ,
DOI : 10.1007/978-3-642-48706-4_16
Sequential updating of conditional probabilities on directed graphical structures. Networks, pp.579-605, 1990. ,
On heuristics for finding loop cutsets in multiply connected belief networks, Uncertainty in Artificial Intelligence, vol.6, pp.233-243, 1991. ,
Probabilistic inference in multiply connected belief networks using loop cutsets, International Journal of Approximate Reasoning, vol.4, issue.4, pp.283-306, 1990. ,
DOI : 10.1016/0888-613X(90)90003-K
A combination of exact algorithms for inference on Bayesian belief networks, International Journal of Approximate Reasoning, vol.5, issue.6, pp.521-542, 1991. ,
DOI : 10.1016/0888-613X(91)90028-K
Initialization for the method of conditioning in Bayesian belief networks, Artificial Intelligence, vol.50, issue.1, pp.83-94, 1991. ,
DOI : 10.1016/0004-3702(91)90091-W
A combination of cutset conditioning with clique-tree propagation in the pathfinder system, Uncertainty in Artificial Intelligence, vol.6, pp.245-253, 1991. ,
Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs, SIAM J. Comput, vol.13, issue.3, pp.566-579, 1984. ,
A note on triangulated graphs and junction trees. Lecture Note, 1992. ,
Inference in bayesian networks using nested junction trees, Statistics, vol.19, pp.301-312, 2000. ,
Inference in multiply sectioned bayesian networks with extended shafer-shenoy and lazy propagation, Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence, pp.680-687, 1999. ,
Inference in multiply sectioned bayesian networks with extended shafer-shenoy and lazy propagation, UAI, vol.43, pp.680-687, 1999. ,
A simple approach to bayesian network computations, Proc. of the Tenth Canadian Conference on Artificial Intelligence, pp.171-178, 1994. ,