A geometric approach to leveraging weak learners

AdaBoost is a popular and effective leveraging procedure for improving the hypotheses generated by weak learning algorithms. AdaBoost and many other leveraging algorithms can be viewed as performing a constrained gradient descent over a potential function. At each iteration the distribution over the sample given to the weak learner is proportional to the direction of steepest descent. We introduce a new leveraging algorithm based on a natural potential function. For this potential function, the direction of steepest descent can have negative components. Therefore, we provide two techniques for obtaining suitable distributions from these directions of steepest descent. The resulting algorithms have bounds that are incomparable to AdaBoost's. The analysis suggests that our algorithm is likely to perform better than AdaBoost on noisy data and with weak learners returning low confidence hypotheses. Modest experiments confirm that our algorithm can perform better than AdaBoost in these situations.