Comparison of the Bayesian and Randomised Decision Tree Ensembles within
  an Uncertainty Envelope Technique
  Multiple Classifier Systems (MCSs) allow evaluation of the uncertainty of
classification outcomes that is of crucial importance for safety critical
applications. The uncertainty of classification is determined by a trade-off
between the amount of data available for training, the classifier diversity and
the required performance. The interpretability of MCSs can also give useful
information for experts responsible for making reliable classifications. For
this reason Decision Trees (DTs) seem to be attractive classification models
for experts. The required diversity of MCSs exploiting such classification
models can be achieved by using two techniques, the Bayesian model averaging
and the randomised DT ensemble. Both techniques have revealed promising results
when applied to real-world problems. In this paper we experimentally compare
the classification uncertainty of the Bayesian model averaging with a
restarting strategy and the randomised DT ensemble on a synthetic dataset and
some domain problems commonly used in the machine learning community. To make
the Bayesian DT averaging feasible, we use a Markov Chain Monte Carlo
technique. The classification uncertainty is evaluated within an Uncertainty
Envelope technique dealing with the class posterior distribution and a given
confidence probability. Exploring a full posterior distribution, this technique
produces realistic estimates which can be easily interpreted in statistical
terms. In our experiments we found out that the Bayesian DTs are superior to
the randomised DT ensembles within the Uncertainty Envelope technique.
