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A Review of Bayesian Networks and Structure Learning
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics. (biostatistics)ORCID iD: 0000-0003-1489-8512
University of Warsaw . (mathematical statistics)
2012 (English)In: Mathematica Applicanda (Matematyka Stosowana), ISSN 2299-4009, Vol. 40, no 1, 51-103 p.Article in journal (Refereed) Published
Abstract [en]

This article reviews the topic of Bayesian networks. A Bayesian networkis a factorisation of a probability distribution along a directed acyclic graph. Therelation between graphicald-separation and independence is described. A short ar-ticle from 1853 by Arthur Cayley [8] is discussed, which contains several ideas laterused in Bayesian networks: factorisation, the noisy ‘or’ gate, applications of algebraicgeometry to Bayesian networks. The ideas behind Pearl’s intervention calculus whenthe DAG represents acausaldependence structure and the relation between the workof 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 onthe assumption offaithfulness, that the data to which the algorithm is applied isgenerated from distributions satisfying a faithfulness assumption where graphicald-separation and independence are equivalent. The article presents some considerationsfor constraint based algorithms based on recent data analysis, indicating a variety ofsituations where the faithfulness assumption does not hold. There is a short discussionabout the causal discovery controversy, the idea thatcausalrelations may be learnedfrom data.

Place, publisher, year, edition, pages
Polish Mathematical Society , 2012. Vol. 40, no 1, 51-103 p.
Keyword [en]
directed acyclic graphs, intervention calulus, Markov graphical models, Markov equivalence
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-137073OAI: diva2:677905
Swedish Research Council, 90583401

QC 20131217

Available from: 2013-12-10 Created: 2013-12-10 Last updated: 2013-12-17Bibliographically approved

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