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142 Algorithm:Learning the Structure of Bayesian Network Classifiers

To conclude, experience shows that the use of independence-based methods in semi-supervised learning is not promising.

Classification Driven Stochastic Structure Search 143

5. Classification Driven Stochastic Structure Search

Definition 7.1 The inverse error measure for structure S′is


where the summation is over the space of possible structures and pS(ˆc(X) ̸= C) is the probability of error of the best classifier learned with structure S.

We use Metropolis-Hastings sampling [Metropolis et al., 1953] to generate samples from the inverse error measure, without having to ever compute it for all possible structures. For constructing the Metropolis-Hastings sampling, we define a neighborhood of a structure as the set of directed acyclic graphs to which we can transit in the next step. Transition is done using a predefined set of possible changes to the structure; at each transition a change consists of a

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