In this note, we discuss the boosting algorithm AdaBoost and identify two
of its main drawbacks: it cannot be used in the boosting by filtering
framework and it is not noise resistant. In order to solve them, we propose a
modification of the weighting system of AdaBoost. We prove that the new
algorithm is in fact a boosting algorithm under the condition that
the sequence of advantages generated by the weak learning algorithm with
respect to the modified distributions is monotonically decreasing. Second, we
show how our algorithm can be used in the boosting by filtering framework
unlike AdaBoost that can only be used in the boosting by subsampling
framework. Finally, we also show that our boosting algorithm is a
statistical query algorithm and thus, it is robust to noise in certain
sense, a property that AdaBoost does not seem to have.