Celebratio Mathematica — Daubechies

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C. Rudin, R. E. Schapire, and I. Daubechies: “Precise statements of convergence for AdaBoost and arc-gv,” pp. 131–145 in Prediction and discovery: AMS-IMS-SIAM joint summer research conference on machine and statistical learning (Snowbird, UT, 25–29 June 2006). Edited by J. S. Verducci, X. Shen, and J. Lafferty. Contemporary Mathematics 443. American Mathematical Society (Providence, RI), 2007. Paper dedicated to Leo Breiman. Available open access here. MR 2433289 Zbl 1141.68722 incollection

We present two main results, the first concerning Freund and Schapire’s AdaBoost algorithm, and the second concerning Breiman’s arc-gv algorithm. Our discussion of AdaBoost revolves around a circumstance called the case of “bounded edges”, in which AdaBoost’s convergence properties can be completely understood. Specifically, our first main result is that if AdaBoost’s “edge” values fall into a small interval, a corresponding interval can be found for the asymptotic margin. A special case of this result closes an open theoretical question of Rätsch and Warmuth. Our main result concerning arc-gv is a convergence rate to a maximum margin solution. Both of these results are derived from an important tool called the “smooth margin”, which is a differentiable approximation of the true margin for boosting algorithms.

Robert Elias Schapire	Related
Leo Breiman	Related
Cynthia Diane Rudin	Related
Xiaotong Shen	Related
Joseph Stephen Verducci	Related
John D. Lafferty	Related

@incollection {key2433289m,
	AUTHOR = {Rudin, Cynthia and Schapire, Robert
		 E. and Daubechies, Ingrid},
	TITLE = {Precise statements of convergence for
		 {A}da{B}oost and arc-gv},
	BOOKTITLE = {Prediction and discovery: {AMS}-{IMS}-{SIAM}
		 joint summer research conference on
		 machine and statistical learning},
	EDITOR = {Verducci, Joseph S. and Shen, Xiaotong
		 and Lafferty, John},
	SERIES = {Contemporary Mathematics},
	NUMBER = {443},
	PUBLISHER = {American Mathematical Society},
	ADDRESS = {Providence, RI},
	YEAR = {2007},
	PAGES = {131--145},
	DOI = {10.1090/conm/443/08559},
	NOTE = {(Snowbird, UT, 25--29 June 2006). Paper
		 dedicated to Leo Breiman. Available
		 open access at http://web.mit.edu/rudin/www/docs/RudinScDa07a.pdf.
		 MR:2433289. Zbl:1141.68722.},
	ISSN = {0271-4132},
	ISBN = {9780821841952},
}