Mixed Bayesian networks are probabilistic models associated with a graphical representation, where the graph is directed and the random variables are discrete or continuous. We propose a comprehensive method for estim...
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Mixed Bayesian networks are probabilistic models associated with a graphical representation, where the graph is directed and the random variables are discrete or continuous. We propose a comprehensive method for estimating the density functions of continuous variables, using a graph structure and a set of samples. The principle of the method is to learn the shape of densities from a sample of continuous variables. The densities are approximated by a mixture of Gaussian distributions. The estimation algorithm is a stochastic version of the Expectation Maximization algorithm (Stochastic EM algorithm). The inference algorithm corresponding to our model is a variant of junction three method, adapted to our specific case. The approach is illustrated by a simulated example from the domain of pharmacokinetics. Tests show that the true distributions seem sufficiently fitted for practical application.
The fundamental result on the rate of convergence of the EM algorithm has proven to be theoretically valuable and practically useful. Here, this result is generalized to the ECM algorithm, a more flexible and applicab...
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The fundamental result on the rate of convergence of the EM algorithm has proven to be theoretically valuable and practically useful. Here, this result is generalized to the ECM algorithm, a more flexible and applicable iterative algorithm proposed recently by Meng and Rubin. Results on the rate of convergence of variations of ECM are also presented. An example is given to show that intuitions accurate for complete-data iterative algorithms may not be trustworthy in the presence of missing data.
This paper deals with the statistical unsupervised image segmentation using fuzzy random fields. We introduce a new fuzzy model containing two components: a ''hard'' component, which describes '...
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This paper deals with the statistical unsupervised image segmentation using fuzzy random fields. We introduce a new fuzzy model containing two components: a ''hard'' component, which describes ''pure'' pixels and a ''fuzzy'' component, which describes ''mixed'' pixels. First, we introduce a procedure to simulate this fuzzy field based on a Gibbs sampler step followed by a second step involving white or correlated Gaussian noises. Then we study the different steps of unsupervised image segmentation. Four different blind segmentation methods are performed: the conditional expectation, two variants of the maximum likelihood, and the least squares approach. As our methods are unsupervised, the parameters required are estimated by the stochastic estimation maximization (sem) algorithm, which is a stochastic variant of the expectation maximization (EM) algorithm, adapted to our model. These ''fuzzy segmentation'' methods are compared ,vith a classical ''hard segmentation'' one, without taking the fuzzy class into account. Our study shows that our ''fuzzy'' sem algorithm provides reliables estimators, especially, regarding the good robustness properties of the segmentation methods. Furthermore, we point out that this ''fuzzy segmentation'' always improves upon the ''hard segmentation'' results.
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