An Adaptive Version of the Boost by Majority Algorithm

The paper describes two methods for finding approximate solutions to the differential equations and a method that results in a provably polynomial time algorithm based on the Newton-Raphson minimization procedure, which is much more efficient in practice but is not known to bePolynomial.

Abstract

We propose a new boosting algorithm. This boosting algorithm is an adaptive version of the boost by majority algorithm and combines bounded goals of the boost by majority algorithm with the adaptivity of AdaBoost. The method used for making boost-by-majority adaptive is to consider the limit in which each of the boosting iterations makes an infinitesimally small contribution to the process as a whole. This limit can be modeled using the differential equations that govern Brownian motion. The new boosting algorithm, named BrownBoost, is based on finding solutions to these differential equations. The paper describes two methods for finding approximate solutions to the differential equations. The first is a method that results in a provably polynomial time algorithm. The second method, based on the Newton-Raphson minimization procedure, is much more efficient in practice but is not known to be polynomial.