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Fast Breaking Comments

By Alexander B. Tsybakov

ESI Special Topics, December 2005
Citing URL - http://www.esi-topics.com/fbp/2005/december05-AlexTsybakov.html

Alexander B. Tsybakov answers a few questions about this month's fast breaking paper in the field of Mathematics.


From •>>December 2005

Field: Mathematics
Article Title: Optimal aggregation of classifiers in statistical learning
Authors: Tsybakov, AB
Journal: ANN STATIST
Volume: 32 (1)
Page: 
Year: FEB 2004
* Univ Paris 06, Lab Probabil & Modeles Aleatoires, 4 Pl Jussieu,Boite Courrier 188, F-75252 Paris 05, France.
* Univ Paris 06, Lab Probabil & Modeles Aleatoires, F-75252 Paris 05, France.

ST:  Why do you think your paper is highly cited?


My paper suggests a mathematical framework that explains high performance of certain classification methods via the fast rates phenomenon.”

Probably because the paper is in a rapidly developing area, at the intersection of statistics and computer science.

ST:  Does it describe a new discovery or a new methodology that's useful to others?

The paper describes the phenomenon of fast rates in pattern classification. It introduces the "margin condition" (now re-baptized as "low noise condition") under which classification with fast rates becomes possible. Furthermore, it shows that fast classifiers can be constructed adaptively, when both the low noise exponent and the complexity of the set of decision boundaries are not known.

ST:  Could you summarize the significance of your paper in layman's terms?

Classification techniques are widely used in many fields; most recent applications include bioinformatics and genomics. The aim of pattern classification is the following: given a training sample that consists of examples and corresponding labels (e.g., class assignments), to predict the class to which a newly arriving example should be assigned. Modern classification methods, such as boosting or Support Vector Machines, often show high efficiency in practice. To achieve this, the parameters that determine these methods should be properly tuned, which is typically done subjectively, in an ad hoc way. My paper suggests a mathematical framework that explains the high performance of certain classification methods via the fast rates phenomenon. It also suggests a methodology of an automatic choice of tuning parameters, free of subjective considerations and leading to fast classification. This is a theoretical paper; it does not come up with immediately realizable recipes for concrete problems, but further work addressing these issues is being rapidly developed.

ST:  How did you become involved in this research?

This research is closely connected to my earlier work on the estimation of sets and boundaries in images (see an overview in A.Korostelev and A.Tsybakov, Lecture Notes in Statistics, vol.82, 1993) and especially to my paper on estimation of level sets (Annals of Statistics, 1997) and to our joint work with Enno Mammen on smooth discrimination analysis (Annals of Statistics, 1999). In these papers, analogs of the "low noise condition" have already been introduced for other closely related statistical problems. A breaking point for me was, at some moment, an essentially obvious observation that classification methods can be used for edge estimation in binary images and vice versa—the only difference appears in the risk criterion.End

Alexandre Tsybakov
Professor
Laboratoire de Probabilites et Modeles Aleatoires
Universite Pierre et Marie Curie
Paris, France

ESI Special Topics, December 2005
Citing URL - http://www.esi-topics.com/fbp/2005/december05-AlexTsybakov.html

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