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Bayesian networks with a logistic regression model for the conditional probabilities. (English) Zbl 1184.62039
Summary: Logistic regression techniques can be used to restrict the conditional probabilities of a Bayesian network for discrete variables. More specifically, each variable of the network can be modeled through a logistic regression model, in which the parents of the variable define the covariates. When all main effects and interactions between the parent variables are incorporated as covariates, the conditional probabilities are estimated without restrictions, as in a traditional Bayesian network. By incorporating interaction terms up to a specific order only, the number of parameters can be drastically reduced. Furthermore, ordered logistic regression can be used when the categories of a variable are ordered, resulting in even more parsimonious models. Parameters are estimated by a modified junction tree algorithm. The approach is illustrated with an Alarm network.

MSC:
62F15 Bayesian inference
62J12 Generalized linear models (logistic models)
65C60 Computational problems in statistics (MSC2010)
Software:
Fahrmeir
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