Bayesian Logic Programs

Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional logic, such as the difficulties to represent objects and relations. We introduce a generalization of Bayesian networks, called Bayesian logic programs, to overcome these limitations. In order to represent objects and relations it combines Bayesian networks with definite clause logic by establishing a one-to-one mapping between ground atoms and random variables. We show that Bayesian logic programs combine the advantages of both definite clause logic and Bayesian networks. This includes the separation of quantitative and qualitative aspects of the model. Furthermore, Bayesian logic programs generalize both Bayesian networks as well as logic programs. So, many ideas developedComment: 52 page

Bayesian networks and decision trees in the diagnosis of female urinary incontinence

This study compares the effectiveness of Bayesian networks versus Decision Trees in modeling the Integral Theory of Female Urinary Incontinence diagnostic algorithm. Bayesian networks and Decision Trees were developed and trained using data from 58 adult women presenting with urinary incontinence symptoms. A Bayesian Network was developed in collaboration with an expert specialist who regularly utilizes a non-automated diagnostic algorithm in clinical practice. The original Bayesian network was later refined using a more connected approach. Diagnoses determined from all automated approaches were compared with the diagnoses of a single human expert. In most cases, Bayesian networks were found to be at least as accurate as the Decision Tree approach. The refined Connected Bayesian Network was found to be more accurate than the Original Bayesian Network accurately discriminated between diagnoses despite the small sample size. In contrast, the Connected and Decision Tree approaches were less able to discriminate between diagnoses. The Original Bayesian Network was found to provide an excellent basis for graphically communicating the correlation between symptoms and laxity defects in a given anatomical zone. Performance measures in both networks indicate that Bayesian networks could provide a potentially useful tool in the management of female pelvic floor dysfunction. Before the technique can be utilized in practice, well-established learning algorithms should be applied to improve network structure. A larger training data set should also improve network accuracy, sensitivity, and specificity

Conjunctive Bayesian networks

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.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6133 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm