We study the problem of learning the best Bayesian network structure with respect to a decomposable score such as BDe, BIC or AIC. This problem is known to be NP-hard, which means that solving it becomes quickly infeasible as the number of variables increases. Nevertheless, in this paper we show that it is possible to learn the best Bayesian network structure with over 30 variables, which cover...

This paper describes research to analyze students’ initial skill level and to predict their hidden characteristics while working with an intelligent tutor. Based only on pre-test problems, a learned network was able to evaluate a students mastery of twelve geometry skills. This model will be used online by an Intelligent Tutoring System to dynamically determine a policy for individualizing sele...

For decomposable score-based structure learning of Bayesian networks, existing approaches first compute a collection of candidate parent sets for each variable and then optimize over this collection by choosing one parent set for each variable without creating directed cycles while maximizing the total score. We target the task of constructing the collection of candidate parent sets when the sc...

In this paper, we present an algorithm for learning structures of Bayesian models in multiple projection spaces. We assume that a visual phenomenon can be projected on a set of spaces that share a common subspace. We propose that models of individual projections can be related through probability distributions over the shared subspace. We develop a learning method that estimates simultaneously ...

Bayesian Constraint-based Causal Discovery (BCCD) is a state-of-the-art method for robust causal discovery in the presence of latent variables. It combines probabilistic estimation of Bayesian networks over subsets of variables with a causal logic to infer causal statements. Currently BCCD is limited to discrete or Gaussian variables. Most of the real-world data, however, contain a mixture of d...

We consider maximin and Bayesian D-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes that a prior distribution for these parameters is available. It was observed empirically by many authors that an increase of uncertainty in the prior information...

Hierarchical latent class (HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are latent. There are no theoretically well justified model selection criteria for HLC models in particular and Bayesian networks with latent nodes in general. Nonetheless, empirical studies suggest that the BIC score is a reasonable criterion to use in practice for le...

The mixed model approach to the analysis of repeated measurements allows users to model the covariance structure of their data. That is, rather than using a univariate or a multivariate test statistic for analyzing effects, tests that assume a particular form for the covariance structure, the mixed model approach allows the data to determine the appropriate structure. Using the appropriate cova...