Name
Abstract | ||
|---|---|---|
This paper studies V-fold cross-validation for model selection in least-squares density estimation. The goal is to provide theoretical grounds for choosing V in order to minimize the least-squares loss of the selected estimator. We first prove a non-asymptotic oracle inequality for V-fold cross-validation and its bias-corrected version (V-fold penalization). In particular, this result implies that V-fold penalization is asymptotically optimal in the nonparametric case. Then, we compute the variance of V-fold cross-validation and related criteria, as well as the variance of key quantities for model selection performance. We show that these variances depend on V like 1 + 4/(V 1), at least in some particular cases, suggesting that the performance increases much from V - 2 to V - 5 or 10, and then is almost constant. Overall, this can explain the common advice to take V - 5 - at least in our setting and when the computational power is limited-, as supported by some simulation experiments. An oracle inequality and exact formulas for the variance are also proved for Monte-Carlo cross-validation, also known as repeated cross-validation, where the parameter V is replaced by the number B of random splits of the data. |
Year | Venue | Keywords |
|---|---|---|
2016 | JOURNAL OF MACHINE LEARNING RESEARCH | V-fold cross-validation,Monte-Carlo cross-validation,leave-one-out,leave-p-out,resampling penalties,density estimation,model selection,penalization |
Field | DocType | Volume |
Least squares,Density estimation,Oracle inequality,Applied mathematics,Artificial intelligence,Asymptotically optimal algorithm,Pattern recognition,Model selection,Nonparametric statistics,Statistics,Cross-validation,Mathematics,Estimator | Journal | 17 |
ISSN | Citations | PageRank |
1532-4435 | 1 | 0.37 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sylvain Arlot | 1 | 65 | 6.87 |
| Matthieu Lerasle | 2 | 4 | 2.49 |