SoloGen

I am wondering what types of regularities are natural to be used in classification problems. In regression setting, different notion of smoothness appears naturally in the bound. I was wondering if I could find similar results for classification.

The field’s landscape is not clear to me yet. People use margin noise conditions that may give them fast rates (faster than n^{-1/2}). If their approach is using a regressor to estimate eta(x) = P{Y=1|X=x}) and then apply a plug-in rule, then the smoothness properties of eta(x) comes to the picture. They may even show that they can get super-fast rates. This smoothness of eta is, however, different from decision surface regularities. Eta can be far from smooth, but the classification might still be easy.

I need to write more about these somewhere, but for now, I found the following Jean-Yves Audibert and Alexandre Tsybakov’s paper interesting:

Jean-Yves Audibert and Alexandre Tsybakov, “Fast Learning Rates for Plug-in Classifiers under the Margin Condition,” Annals of Statistics, 2007.

Also I guess it would be nice to read the following paper too:

Michael Kohler and Adam Kryzak, “On the Rate of Convergence of Local Averaging Plug-in Classification Rules under a Margin Condition,” 2006.

Mar 17