Name
Abstract | ||
|---|---|---|
We consider the binary classification problem. Given an i.i.d. sample drawn from the distribution of an X ×{ 0, 1}−valued random pair, we propose to estimate the so-called Bayes classifier by minimizing the sum of the empirical classification error and a penalty term based on Efron's or i.i.d. weighted bootstrap samples of the data. We obtain exponential inequalities for such bootstrap type penalties, which allow us to derive non-asymptotic proper- ties for the corresponding estimators. In particular, we prove that these estimators achieve the global minimax risk over sets of functions built from Vapnik-Chervonenkis classes. The ob- tained results generalize Koltchinskii (2001) and Bartlett et al.'s (2002) ones for Rademacher penalties that can thus be seen as special examples of bootstrap type penalties. To illustrate this, we carry out an experimental study in which we compare the different methods for an intervals model selection problem. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s10994-006-7679-y | Machine Learning |
Keywords | Field | DocType |
Model selection,Classification,Bootstrap penalty,Exponential inequality,Oracle inequality,Minimax risk | Discrete mathematics,Mathematical optimization,Minimax,Exponential function,Binary classification,Bootstrapping,Model selection,Mathematics,Bootstrapping (electronics),Bayes classifier,Estimator | Journal |
Volume | Issue | ISSN |
66 | 2-3 | 0885-6125 |
Citations | PageRank | References |
6 | 0.69 | 11 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Magalie Fromont | 1 | 13 | 2.24 |