for the birth and change moves, respectively.

Because of the hierarchical structure, new moves applied to the first partition levels can heavily change the shape of the DT and, as a result, at its bottom partitions the terminal nodes can contain fewer data points than pmin. However, if the DT contains one such node, we can sweep it and then make the death move. Less likely, after birth or change moves the DT will contain more than one node containing fewer than pmin data points. In such cases we have to resample the DT. 

## 3. Selection Of A Single Dt

In this Section we describe our method of interpreting Bayesian DT ensembles. This method is based on the estimates of confidence in the outcomes of the DT ensemble which can be quantitatively estimated on the training data within the Uncertainty Envelope technique. 

## 3.1. Selection Techniques

There are two approaches to interpreting DT ensembles. The first approach is based on searching a DT of MAP [11]. The second approach is based on the idea of clustering DTs in the two-dimensional space of DT size and DT fitness [12]. 

Our approach is based on the quantitative estimates of classification confidence, which can be made within the Uncertainty Envelope technique described in [9]. The idea behind our method of interpreting the Bayesian DT ensemble is to find a single DT which covers most of the training examples classified as confident and correct. For multiple classification systems the confidence of classification outputs can be easily estimated by counting the consistency of the classification outcomes. 

Indeed, within a given classification scheme the outputs of the multiple classifier system depend on how well the classifiers were trained and how representative were the training data. For a given data sample, the consistency of classification outcomes depends on how close this sample is to the class boundaries. So for the ith class, the confidence in the set of classification models can be estimated as a ratio i between the number of classifier outcomes of the ith class, Ni, and the total number of classifiers N: 
 i = Ni /N, i = 1, …, C, where C is the number of classes.

Clearly the classification confidence is maximal, equal to 1.0, if all the classifiers assign a given input to the same class, otherwise the confidence is less than 1.0. The minimal value of confidence is equal to 1/C if the classifiers assign the input datum to the C classes in equal proportions. So for a given input the classification confidence in the set of classifiers can be properly estimated by the ratio . 

Within the above framework in real-world applications, we can define a given level of the classification confidence, 0: 1/C ≤ 0 ≤ 1, for which cost of misclassification is small enough to be accepted. Then for the given input, the outcome of the set of classifiers is said to be *confident* if the ratio  ≥ 0. Clearly, on the labeled data we can distinguish between *confident and correct* outcomes and *confident but* incorrect outcomes. The latter outcomes may appear in a multiple classifier system due to noise or overlapping classes in the data. 

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