Celebratio Mathematica — Daubechies

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C. Rudin, I. Daubechies, and R. Schapire: “On the dynamics of boosting” in Advances in neural information processing systems 16: Proceedings of the 2003 conference (Vancouver and Whistler, BC, 8–13 December 2003). Edited by S. Thrun, L. K. Saul, and B. Schölkopf. MIT Press (Cambridge, MA), 2004. incollection

In order to understand AdaBoost’s dynamics, especially its ability to maximize margins, we derive an associated simplified nonlinear iterated map and analyze its behavior in low-dimensional cases. We find stable cycles for these cases, which can explicitly be used to solve for AdaBoost’s output. By considering AdaBoost as a dynamical system, we are able to prove Ratsch and Warmuth’s conjecture that AdaBoost may fail to converge to a maximal-margin combined classifier when given a ‘nonoptimal’ weak learning algorithm. AdaBoost is known to be a coordinate descent method, but other known algorithms that explicitly aim to maximize the margin (such as AdaBoost* and arc-gv) are not. We consider a differentiable function for which coordinate ascent will yield a maximum margin solution. We then make a simple approximation to derive a new boosting algorithm whose updates are slightly more aggressive than those of arc-gv.

Lawrence Kevin Saul	Related
Robert Elias Schapire	Related
Sebastian Thrun	Related
Bernhard Schölkopf	Related
Cynthia Diane Rudin	Related