Celebratio Mathematica — Daubechies

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C. Rudin, R. E. Schapire, and I. Daubechies: “Boosting based on a smooth margin,” pp. 502–517 in Learning theory: 17th annual conference on learning theory (Banff, AB, 1–4 July 2004). Edited by J. Shawe-Taylor and Y. Singer. Lecture Notes in Computer Science 3120. Springer (Berlin), 2004. MR 2177931 Zbl 1078.68724 incollection

We study two boosting algorithms, Coordinate Ascent Boosting and Approximate Coordinate Ascent Boosting, which are explicitly designed to produce maximum margins. To derive these algorithms, we introduce a smooth approximation of the margin that one can maximize in order to produce a maximum margin classifier. Our first algorithm is simply coordinate ascent on this function, involving a line search at each step. We then make a simple approximation of this line search to reveal our second algorithm. These algorithms are proven to asymptotically achieve maximum margins, and we provide two convergence rate calculations. The second calculation yields a faster rate of convergence than the first, although the first gives a more explicit (still fast) rate. These algorithms are very similar to AdaBoost in that they are based on coordinate ascent, easy to implement, and empirically tend to converge faster than other boosting algorithms. Finally, we attempt to understand AdaBoost in terms of our smooth margin, focusing on cases where AdaBoost exhibits cyclic behavior.

Robert Elias Schapire	Related
Cynthia Diane Rudin	Related
John Stewart Shawe-Taylor	Related
Yoram Singer	Related