Large Margin Trees for Induction and Transduction
The problem of controlling the capacity of decision trees is considered for the case where the decision nodes implement linear threshold functions. In addition to the standard early stopping and pruning procedures, we implement a strategy based on the margins of the decision boundaries at the nodes. The approach is motivated by bounds on generalization error obtained in terms of the margins of the individual classifiers. Experimental results are given which demonstrate that considerable advantage can be derived from using the margin information. The same strategy is applied to the problem of transduction, where the positions of the testing points are revealed to the training algorithm. This information is used to generate an alternative training criterion motivated by transductive theory. In the transductive case, the results are not as encouraging, suggesting that little, if any, consistent advantage is culled from using the unlabelled data in the proposed fashion. This conclusion does not contradict theoretical results, but leaves open the theoretical and practical question of whether more effective use can be made of the additional information.