The AdaBoost Flow

AdaBoost algorithm does not need an advertisement in data mining community. It was discovered by Robert Schapire and Yoav Freund in their seminal paper in 1997. Nowadays together with PageRank algorithm AdaBoost is considered among top ten algorithm in data mining. It is worth mentioning that for their AdaBoost paper Schapire and Freund won the Godel Prize, which is one of the most prestigious awards in theoretical computer science, in the year of 2003.
In this talk we introduce a dynamical system which we call the AdaBoost flow. The flow is defined by a system of ODEs with control. We show how by a suitable choice of control AdaBoost algorithm of Schapire and Freund can be embedded into the AdaBoost flow. The AdaBoost flow equations coincide with the equations of dynamics of the nonperiodic Toda system written in terms of spectral variables. This establishes a connection between two seemingly unrelated fields of boosting algorithms and classical integrable models. Finally we explain similarity of the AdaBoost flow with Perelman's ideas to control Ricci flow.