Square root penalty: Adaptation to the margin in classification and in edge estimation

Tsybakov, A. B.; van de Geer, S. A.

Ann. Statist., Tome 33 (2005) no. 1, p. 1203-1224 / Harvested from Project Euclid

Résumé

We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the excess risk, that is, rates that can be faster than n^−1/2, where n is the sample size. We show that our method also gives adaptive estimators for the problem of edge estimation.

Publié le : 2005-06-14
Classification: Binary classification, edge estimation, adaptation, margin, penalized classification rule, square root penalty, sparsity, block thresholding, 62G07, 62G08, 62H30, 68T10

@article{1120224100,
     author = {Tsybakov, A. B. and van de Geer, S. A.},
     title = {Square root penalty: Adaptation to the margin in classification and in edge estimation},
     journal = {Ann. Statist.},
     volume = {33},
     number = {1},
     year = {2005},
     pages = { 1203-1224},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1120224100}
}

Tsybakov, A. B.; van de Geer, S. A. Square root penalty: Adaptation to the margin in classification and in edge estimation. Ann. Statist., Tome 33 (2005) no. 1, pp.  1203-1224. http://gdmltest.u-ga.fr/item/1120224100/