Geodesic
A Review of Bayesian Networks and Structure Learning
Mathematica Applicanda, Tome 40 (2012) no. 1, pp. 51-103.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

This article reviews the topic of Bayesian networks. A Bayesian network is a factorisation of a probability distribution along a directed acyclic graph. The relation between graphical d-separation and independence is described. A short article by Arthur Cayley (1853) [7] is discussed, which laid ideas later used in Bayesian networks: factorisation, the noisy `or' gate, applications of algebraic geometry to Bayesian networks. The ideas behind Pearl's intervention calculus when the DAG represents a causal dependence structure; the relation between the work of Cayley and Pearl is commented on.Most of the discussion is about structure learning, outlining the two main approaches; search and score versus constraint based. Constraint based algorithms often rely on the assumption of faithfulness, that the data to which the algorithm is applied is generated from distributions satisfying a faithfulness assumption where graphical d- separation and independence are equivalent. The article presents some considerations for constraint based algorithms based on recent data analysis, indicating a variety of situations where the faithfulness assumption does not hold.
DOI : 10.14708/ma.v40i1.278
Classification : 62H05, 68T37, 65S05
Mots-clés : Bayesian networks, directed acyclic graph, Arthur Cayley, intervention calculus, graphical Markov model, Markov equivalence, structure learning 
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Timo J.T. Koski; John Noble. A Review of Bayesian Networks and Structure Learning. Mathematica Applicanda, Tome 40 (2012) no. 1, pp.  51-103. doi : 10.14708/ma.v40i1.278. http://geodesic.mathdoc.fr/articles/10.14708/ma.v40i1.278/

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