.png){kind=icon}
返回
CONDITIONAL PREDICTIVE INFERENCE FOR STABLE ALGORITHMS
.png){kind=icon}
OA
AI
DOI：10.1214/22-AOS2250.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
We investigate generically applicable and intuitively appealing predic-tion intervals based on k-fold cross-validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training sample (hence, training conditional validity), and show that it is close to the nominal level, in an appropriate sense, provided that the underlying algorithm used for computing point predictions is sufficiently stable when feature-response pairs are omitted. Our results are based on a finite sam-ple analysis of the empirical distribution function of k-fold cross-validation residuals and hold in nonparametric settings with only minimal assumptions on the error distribution. To illustrate our results, we also apply them to high -dimensional linear predictors, where we obtain uniform asymptotic training conditional validity as both sample size and dimension tend to infinity at the same rate and consistent parameter estimation typically fails. These results show that despite the serious problems of resampling procedures for infer-ence on the unknown parameters (cf. in A Festschrift for Erich L. Lehmann (1983) 28???48 Wadsworth; Ann. Statist. 24 (1996) 307???335; J. Mach. Learn. Res. 19 (2018) 5), cross-validation methods can be successfully applied to ob-tain reliable predictive inference even in high dimensions and conditionally on the training data.
Keyword:
Prediction intervals
high-dimensional regression
algorithmic stability
cross-validation
期刊
IF:
3.7
论文数:
2.8K
被引数:
2.9W
机构
引用论文
.png){kind=icon}
查看更多内容