The AdaBoost Flow

We introduce a dynamical system that we call the AdaBoost flow. The flow is defined by a system of ODEs with control. We show that three algorithms of the AdaBoost family, (i) the AdaBoost algorithm of Schapire and Freund, (ii) the arc‐gv algorithm of Breiman, and (iii) the confidence rated prediction of Schapire and Singer, can be embedded in the AdaBoost flow. The nontrivial part of the AdaBoost flow equations coincides with the equations of dynamics of the nonperiodic Toda system written in terms of spectral variables. We provide a novel invariant geometrical description of the AdaBoost algorithm as a gradient flow on a foliation defined by level sets of the potential function. We propose a new approach for constructing boosting algorithms as a continuous‐time gradient flow on measures defined by various metrics and potential functions. Finally, we explain the similarity of the AdaBoost algorithm with the Perelman's construction for the Ricci flow.© 2015 Wiley Periodicals, Inc.