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Some Open Problems in Optimal AdaBoost and Decision Stumps
Answers to the open problems can have immediate significant impact to (1) cementing previously established results on asymptotic convergence properties of Optimal AdaBoost, for finite datasets, which in turn can be the start to any convergence-rate analysis; (2) understanding the weak-hypotheses class of effective decision stumps generated from data, which we have empirically observed to be significantly smaller than the typically obtained class, as well as the effect on the weak learner's running time and previously established improved bounds on the generalization performance of Optimal AdaBoost classifiers; and (3) shedding some light on the "self control" that AdaBoost tends to exhibit in practice.
On the Convergence Properties of Optimal AdaBoost
We provide constructive proofs of several arbitrarily accurate approximations of Optimal AdaBoost; prove that they exhibit certain cycling behavior in finite time, and that the resulting dynamical system is ergodic; and establish sufficient conditions for the same to hold for the actual Optimal-AdaBoost update.
