We investigate popular resampling methods for estimating the uncertainty of statistical models, such as subsampling, bootstrap and the jackknife, and their performance in high-dimensional supervised regression tasks. We provide a tight asymptotic description of the biases and variances estimated by these methods in the context of generalized linear models, such as ridge and logistic regression, taking the limit where the number of samples $n$ and dimension $d$ of the covariates grow at a comparable fixed rate $\alpha\!=\! n/d$. Our findings are three-fold: i) resampling methods are fraught with problems in high dimensions and exhibit the double-descent-like behavior typical of these situations; ii) only when $\alpha$ is large enough do they provide consistent and reliable error estimations (we give convergence rates); iii) in the over-parametrized regime $\alpha\!<\!1$ relevant to modern machine learning practice, their predictions are not consistent, even with optimal regularization.

翻译：我们研究了用于估计统计模型不确定性的流行重采样方法，如子采样、自助法和刀切法，及其在高维监督回归任务中的表现。我们在广义线性模型（如岭回归和逻辑回归）的背景下，对这些方法估计的偏差和方差给出了严格的渐近描述，其中样本数 $n$ 与协变量维度 $d$ 以可比的固定速率 $\alpha\!=\! n/d$ 增长。我们的发现有三方面：i) 重采样方法在高维情况下问题重重，并表现出此类情况下典型的双下降类行为；ii) 仅当 $\alpha$ 足够大时，它们才能提供一致且可靠的误差估计（我们给出了收敛速率）；iii) 在与现代机器学习实践相关的过参数化区域 $\alpha\!<\!1$ 中，即使采用最优正则化，它们的预测也不具有一致性。