We improve the analysis of the decision tree boosting algorithm proposed by Mansour and McAllester. For binary classification problems, the algorithm of Mansour and McAllester constructs a multi-way branching decision tree using a set of multi-class hypotheses. Mansour and McAllester proved that it works under certain conditions. We give a rigorous analysis of the algorithm and simplify the conditions. From this simplification, we can provide a simpler algorithm, for which no prior knowledge on the quality of weak hypotheses is necessary.
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