Oracle bounds and exact algorithm for dyadic classification trees

This paper introduces a new method using dyadic decision trees for estimating a classification or a regression function in a multi-class classification problem. The estimator is based on model selection by penalized empirical loss minimization. Our work consists in two complementary parts: first, a theoretical analysis of the method leads to deriving oracle-type inequalities for three different possible loss functions. Secondly, we present an algorithm able to compute the estimator in an exact way.