Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Convergence Properties of Optimal AdaBoost   AdaBoost is one of the most popular machine-learning algorithms. It is simple
to implement and often found very effective by practitioners, while still being
mathematically elegant and theoretically sound. AdaBoost's behavior in
practice, and in particular the test-error behavior, has puzzled many eminent
researchers for over a decade: It seems to defy our general intuition in
machine learning regarding the fundamental trade-off between model complexity
and generalization performance. In this paper, we establish the convergence of
"Optimal AdaBoost," a term coined by Rudin, Daubechies, and Schapire in 2004.
We prove the convergence, with the number of rounds, of the classifier itself,
its generalization error, and its resulting margins for fixed data sets, under
certain reasonable conditions. More generally, we prove that the time/per-round
average of almost any function of the example weights converges. Our approach
is to frame AdaBoost as a dynamical system, to provide sufficient conditions
for the existence of an invariant measure, and to employ tools from ergodic
theory. Unlike previous work, we do not assume AdaBoost cycles; actually, we
present empirical evidence against it on real-world datasets. Our main
theoretical results hold under a weaker condition. We show sufficient empirical
evidence that Optimal AdaBoost always met the condition on every real-world
dataset we tried. Our results formally ground future convergence-rate analyses,
and may even provide opportunities for slight algorithmic modifications to
optimize the generalization ability of AdaBoost classifiers, thus reducing a
practitioner's burden of deciding how long to run the algorithm.

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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys