Decision Forests - Data Mining with Decision Trees: Theory and Applications - page 125

In fact bagging can be considered to be wagging with allocation of
weights from the Poisson distribution (each instance is represented in the
sample a discrete number of times). Alternatively, it is possible to allocate
the weights from the exponential distribution, because the exponential
distribution is the continuous valued counterpart to the Poisson distribution
[ Webb (2000) ] .
9.4.2.3 Random Forest
A Random Forest ensemble uses a large number of individual, unpruned
decision trees which are created by randomizing the split at each node of
the decision tree [Breiman (2001)]. Each tree is likely to be less accurate
than a tree created with the exact splits. But, by combining several of
these “approximate” trees in an ensemble, we can improve the accuracy,
often doing better than a single tree with exact splits.
The individual trees are constructed using the algorithm presented
in Figure 9.13. The input parameter N represents the number of input
variables that will be used to determine the decision at a node of the tree.
This number should be much less than the number of attributes in the
training set. Note that bagging can be thought of as a special case of random
forests obtained when N is set to the number of attributes in the original
training set. The IDT in Figure 9.13 represents any top-down decision tree
induction algorithm with the following modification: the decision tree is
not pruned and at each node, rather than choosing the best split among all
attributes, the IDT randomly samples N of the attributes and chooses the
best split from among those variables. The classification of an unlabeled
instance is performed using majority vote.
Fig. 9.13 The random forest algorithm.