Suboptimality of Penalized Empirical Risk Minimization in Classification
| dc.creator | Lecué, Guillaume | |
| dc.date | 2007-03-27 | |
| dc.date.accessioned | 2026-07-07T12:07:24Z | |
| dc.date.available | 2026-07-07T12:07:24Z | |
| dc.description | Let $\cF$ be a set of $M$ classification procedures with values in $[-1,1]$. Given a loss function, we want to construct a procedure which mimics at the best possible rate the best procedure in $\cF$. This fastest rate is called optimal rate of aggregation. Considering a continuous scale of loss functions with various types of convexity, we prove that optimal rates of aggregation can be either $((\log M)/n)^{1/2}$ or $(\log M)/n$. We prove that, if all the $M$ classifiers are binary, the (penalized) Empirical Risk Minimization procedures are suboptimal (even under the margin/low noise condition) when the loss function is somewhat more than convex, whereas, in that case, aggregation procedures with exponential weights achieve the optimal rate of aggregation. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703811 | |
| dc.identifier | http://arxiv.org/abs/math/0703811 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208955 | |
| dc.subject | Statistics Theory | |
| dc.subject | Risk Management | |
| dc.subject | 62G05 | |
| dc.title | Suboptimality of Penalized Empirical Risk Minimization in Classification | |
| dc.type | text |