A single decision tree can learn quite complex functions. However, in many ways it will be prone to overfitting—learning rules that work only for the training set. One of the ways that we can adjust for this is to limit the number of rules that it learns. For instance, we could limit the depth of the tree to just three layers. Such a tree will learn the best rules for splitting the dataset at a global level, but won't learn highly specific rules that separate the dataset into highly accurate groups. This trade-off results in trees that may have a good generalization, but overall slightly poorer performance.

To compensate for this, we could create many decision trees and then ask each to predict the class value. We could take a majority vote and use that answer as our overall prediction. Random forests work on this principle.

There are two problems with the aforementioned procedure. The first problem is that building decision trees is largely deterministic—using the same input...