Conjunctive Bayesian networks

Details Conjunctive Bayesian networks Conjunctive Bayesian networks

2006-08-16

arxiv.org/abs/math/0608417v4

Bernoulli 2007, Vol. 13, No. 4, 893-909

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/07-BEJ6133 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6133

Conjunctive 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 Gr\"{o}bner basis.

Affiliated with

Also associated with

No associations

Rating

Conjunctive Bayesian networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Conjunctive Bayesian networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conjunctive Bayesian networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-220517