document: Mining optimal decision trees from itemset lattices We present DL8 , an exact algorithm for finding a decision tree that optimizes a ranking function under size , depth , accuracy and leaf constraints . Because the discovery of optimal trees has high theoretical complexity , until now few efforts have been made to compute such trees for real-world datasets . An exact algorithm is of both scientific and practical interest . From a scientific point of view , it can be used as a gold standard to evaluate the performance of heuristic constraint-based decision tree learners and to gain new insight in traditional decision tree learners . From the application point of view , it can be used to discover trees that can not be found by heuristic decision tree learners . The key idea behind our algorithm is that there is a relation between constraints on decision trees and constraints on itemsets . We show that optimal decision trees can be extracted from lattices of itemsets in linear time . We give several strategies to efficiently build these lattices . Experiments show that under the same constraints , DL8 obtains better results than C4 .5 , which confirms that exhaustive search does not always imply overfitting . The results also show that DL8 is a useful and interesting tool to learn decision trees under constraints .
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