2007/01/19 by Sylvain Arlot, Arlot, Sylvain
Computer Science · Engineering · #62G08 #62G09 #Control Systems and Identification #FOS: Mathematics #Fault Detection and Control Systems #Machine Learning and Data Classification #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.math/0701542
openalex publication_date 2007/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new family of model selection algorithms based on the resampling heuristics. It can be used in several frameworks, do not require any knowledge about the unknown law of the data, and may be seen as a generalization of local Rademacher complexities and V-fold cross-validation. In the case example of least-square regression on histograms, we prove oracle inequalities, and that these algorithms are naturally adaptive to both the smoothness of the regression function and the variability of the noise level. Then, interpretating V-fold cross-validation in terms of penalization, we enlighten the question of choosing V. Finally, a simulation study illustrates the strength of resampling penalization algorithms against some classical ones, in particular with heteroscedastic data.