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TitleConjunctive Bayesian networks.
Author(s) Niko Beerenwinkel, Nicholas Eriksson, Bernd Sturmfels
TypeArticle in Journal
AbstractConjunctive Bayesian networks (CBNs) are graphical models that describe the accumulation of events which are constrained in the order of their occurrence. A CBN is given by a partial order on a (finite) set of events. CBNs generalize the oncogenetic tree models of Desper et al. by allowing the occurrence of an event to depend on more than one predecessor event. The present paper studies the statistical and algebraic properties of CBNs. We determine the maximum likelihood parameters and present a combinatorial solution to the model selection problem. Our method performs well on two datasets where the events are HIV mutations associated with drug resistance. Concluding with a study of the algebraic properties of CBNs, we show that CBNs are toric varieties after a coordinate transformation and that their ideals possess a quadratic Gröbner basis.
ISSN1350-7265
URL http://projecteuclid.org/euclid.bj/1194625594
LanguageEnglish
JournalBernoulli
Volume13
Number4
Pages893--909
PublisherInternational Statistical Institute (ISI), Voorburg; Bernoulli Society for Mathematical Statistics a
Year2007
Edition0
Translation No
Refereed No
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