Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
The EM algorithm for graphical association models with missing data
Computational Statistics & Data Analysis - Special issue dedicated to Toma´sˇ Havra´nek
Local learning in probabilistic networks with hidden variables
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Efficient approximations for the marginal likelihood of incomplete data given a Bayesian network
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Efficient Approximations for the MarginalLikelihood of Bayesian Networks with Hidden Variables
Machine Learning - Special issue on learning with probabilistic representations
A Probabilistic Framework for the Hierarchic Organisation and Classification of Document Collections
Journal of Intelligent Information Systems
Learning Hidden Variable Networks: The Information Bottleneck Approach
The Journal of Machine Learning Research
Review: learning bayesian networks: Approaches and issues
The Knowledge Engineering Review
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Recursive graphical models usually underlie the statistical modelling concerning probabilistic expert systems based on Bayesian networks. This paper defines a version of these models, denoted as recursive exponential models, which have evolved by the desire to impose sophisticated domain knowledge onto local fragments of a model. Besides the structural knowledge, as specified by a given model, the statistical modelling may also include expert opinion about the values of parameters in the model. It is shown how to translate imprecise expert knowledge into approximately conjugate prior distributions. Based on possibly incomplete data, the score and the observed information are derived for these models. This accounts for both the traditional score and observed information, derived as derivatives of the log-likelihood, and the posterior score and observed information, derived as derivatives of the log-posterior distribution. Throughout the paper the specialization into recursive graphical models is accounted for by a simple example.