An Analysis of Reduced Error Pruning

Top-down induction of decision trees has been observed to suer from the inadequate functioning of the pruning phase. In particular, it is known that the size of the resulting tree grows linearly with the sample size, even though the accuracy of the tree does not improve. Reduced Error Pruning is an algorithm that has been used as a representative technique in attempts to explain the problems of decision tree learning. In this paper we present analyses of Reduced Error Pruning in three dierent settings. First we study the basic algorithmic properties of the method, properties that hold inde-pendent of the input decision tree and pruning examples. Then we examine a situation that intuitively should lead to the subtree under consideration to be replaced by a leaf node, one in which the class label and attribute values of the pruning examples are independent of each other. This analysis is conducted under two dierent assumptions. The general analysis shows that the pruning probability of a node tting pure noise is bounded by a function that decreases exponentially as the size of the tree grows. In a specic analysis we assume that the examples are distributed uniformly to the tree. This assumption lets us approximate the number of subtrees that are pruned because they do not receive any pruning examples. This paper claries the dierent variants of the Reduced Error Pruning algorithm, brings new insight to its algorithmic properties, analyses the algorithm with less imposed assumptions than before, and includes the previously overlooked empty subtrees to the analysis. 1