Bayesian classification (AutoClass): theory and results
Advances in knowledge discovery and data mining
Efficient Approximations for the MarginalLikelihood of Bayesian Networks with Hidden Variables
Machine Learning - Special issue on learning with probabilistic representations
Hierarchical latent class models for cluster analysis
Eighteenth national conference on Artificial intelligence
On the geometry of Bayesian graphical models with hidden variables
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Asymptotic model selection for directed networks with hidden variables*
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Algebraic statistics in model selection
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Classification using Hierarchical Naïve Bayes models
Machine Learning
Latent tree models and diagnosis in traditional Chinese medicine
Artificial Intelligence in Medicine
Effective dimensions of hierarchical latent class models
Journal of Artificial Intelligence Research
Effective dimensions of partially observed polytrees
International Journal of Approximate Reasoning
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Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When hidden variables are present, however, standard dimension might no longer be appropriate. One should instead use effective dimension (Geiger et al. 1996). This paper is concerned with the computation of effective dimension. First we present an upper bound on the effective dimension of a latent class (LC) model. This bound is tight and its computation is easy. We then consider a generalization of LC models called hierarchical latent class (HLC) models (Zhang 2002). We show that the effective dimension of an HLC model can be obtained from the effective dimensions of some related LC models. We also demonstrate empirically that using effective dimension in place of standard dimension improves the quality of models learned from data.