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... | @@ -17,4 +17,10 @@ Steps of Hill-Climbing algorithm: |
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5. Stops when the value changes less than the threshold value.
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5. Stops when the value changes less than the threshold value.
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The following score functions from [BAMT package](https://github.com/ITMO-NSS-team/BAMT) are included in Web BAMT: K2, BIC (Bayesian Information Criterion), MI (Mutual Information).
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The following score functions from [BAMT package](https://github.com/ITMO-NSS-team/BAMT) are included in Web BAMT: K2, BIC (Bayesian Information Criterion), MI (Mutual Information).
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The above approach to structure search allows to introduce elements of expert control by narrowing the search area to structures that include expert-specified edges or fixed root nodes describing key and basic features. |
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The above approach to structure search allows to introduce elements of expert control by narrowing the search area to structures that include expert-specified edges or fixed root nodes describing key and basic features.
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# Parametric learning algorithms for the Bayesian network
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Parametric learning of distributions is performed by the method of likelihood maximization in a fixed class of distributions. In classical conditional Gaussian Bayesian networks, multinomial discrete distributions are used to describe discrete features and Gaussian distributions are used to approximate continuous ones.
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One of the extensions to this basic model available in Web BAMT is the application of a multinomial mixture of Gaussian distributions.
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BIC and AIC criterion-based approach is used to determine the number of mixture components. Parameter learning of such a model is also done by the method of likelihood maximization. Due to the large number of unknowns, an EM algorithm is used to find the model parameters, which consists of two steps: an estimation step in which we estimate the posterior probabilities of the mixture, and a maximization step in which we recalculate the mixture parameters to maximize the posterior probabilities.
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Another available modification is including classification models, in this implementation such models are represented by logistic regression (logit). In general, Bayesian network structure learning methods allow continuous variables to be parents of discrete variables. The main problem arises at the parameter learning stage, as such parent-child pairs imply a model that estimates a discrete distribution with respect to some continuous data. However, these types of relationships can be specified expertly and ignoring them may affect the quality and interpretability of the model. |
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