  Two popular boosted decsion tree (BDT) methods, Adaptive BDT (AdaBDT) and
Gradient BDT (GradBDT) are studied in the classification problem of separating
signal from background assuming all trees are weak learners. The following
results are obtained. a) The distribution of the BDT score is approximately
Gaussian for both methods. b) With more trees in training, the distance of the
expectaion of score distribution between signal and background is larger, but
the variance of both distributions becomes greater at the same time. c)
Extenstion of the boosting mechanism in AdaBDT to any loss function is
possible. d) AdaBDT is shown to be equivalent to the GradBDT with 2 terminal
nodes for a decision tree. In the field high energy physics, many applications
persue the best statistical significance. We also show that the maximization of
the statistical significance is closely related to the minimization of the loss
function, which is the target of the BDT algorithms.
