A Review of Bayesian Networks and Structure Learning
2012 (English)In: Mathematica Applicanda (Matematyka Stosowana), ISSN 2299-4009, Vol. 40, no 1, 51-103 p.Article in journal (Refereed) Published
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  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.
directed acyclic graphs, intervention calulus, Markov graphical models, Markov equivalence
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-137073OAI: oai:DiVA.org:kth-137073DiVA: diva2:677905
FunderSwedish Research Council, 90583401
QC 201312172013-12-102013-12-102013-12-17Bibliographically approved