We introduce a dynamical system which we call the AdaBoost flow. The flow isView original: http://arxiv.org/abs/1110.6228
defined by a system of ODEs with control. We show how by a suitable choice of
control the AdaBoost algorithm of Schapire and Freund and the arc-gv algorithm
of Breiman can be embedded in the AdaBoost flow. We also show how confidence
rated prediction previously studied by Schapire and Singer also can be obtained
from our continuous time approach. We introduce a new continuous time algorithm
which we call superBoost and describe its properties.
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. This establishes a connection between the two seemingly
unrelated fields of boosting algorithms and exactly soluble models of classical
mechanics. Finally we explain the similarity of the AdaBoost construction with
Perelman's ideas to control the Ricci flow.