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to overtraining may be partially removed by the pruning (removing of statistically
insignificant nodes) of decision trees.
The advantage of the boosted decision tree method is its transparency and little tuning
requirement. Inclusion of poorly discriminating input variables does not hurt
the method in any way, while it may cause problems for other methods. Though in
theory boosted decision tree should underperform in comparison to other, more theoretically
advanced methods, in practice in many cases it is working better because
either there are not enough training events to properly populate multi dimensional
probability density function or the neural network architecture has not been correctly
optimised. The main advantage of boosted decision tree method, in spite of
its slowness and memory demand, is the simplicity and easiness of usage.
All the methods described above have been to some extend trained and tested for their
possible application in this analysis. All of them appeared to explore comparable discriminating
performance, with some being significantly slower. The results obtained with two
most efficient methods: maximum likelihood and neural network agree within 2%.
One way to compare the performance of the different classifiers is to plot signal efficiency
and background rejection determined for any possible cut introduced on the discriminator.
The example of such a comparison for the first MVA bin in E γ T
and the CB1 wheel is
presented in figure 1. The further the graph tends towards the upper right corner (high
signal efficiency, high background rejection power), the better the classifier. In the case
of this analysis though all the classifiers perform equally well with the sole exception of
the Support Vector Machine method, which probably was not tuned well enough.
Background rejection
1
0.8
0.6
0.4
0.2
5.0 < E T
Likelihood
Range Search
k-Nearest Neighbour
Fisher discriminant
Neural Network
Support Vector Machine
Boosted Decision Tree
< 5.5 GeV
CB1
0
0 0.2 0.4 0.6 0.8 1
Signal efficiency
Figure 1: The signal efficiency versus background rejection graph for all studied classifiers
in the first MVA E T bin and the CB1 wheel.