The forest error rate in Random forest depends on the following two factors:
1. How correlated the two trees in the forest are i.e,
The correlation between any two different trees in the forest. Increasing the correlation increases the forest error rate.
2. How strong each individual tree in the forest is i.e,
The strength of each individual tree in the forest. In a forest, a tree having a low error rate is considered a strong classifier. Increasing the strength of the individual trees eventually leads to a decrement in the forest error rate.
Moreover, reducing the value of mtry i.e, the number of random variables used in each tree reduces both the correlation and the strength. Increasing it increases both. So, in between, there exists an “optimal” range of mtry which is usually quite a wide range.
Using the OOB error rate, a value of mtry can quickly be found in the range. This parameter is only adjustable from which random forests are somewhat sensitive.