标题： 同时分析近似留一交叉验证和平均场推断 显示英文标题

标题： Simultaneous analysis of approximate leave-one-out cross-validation and mean-field inference

摘要： 近似留一交叉验证（ALO-CV）是一种被提出的方法，用于估计高维情况下正则化估计量的泛化误差，其中维度和样本量处于同一数量级，即所谓的“比例情形”。 开发了一种新的分析方法，在高斯协变量和正则化项的强凸性条件下，推导出非可微正则化项下ALO-CV的一致性。 通过条件论证，展示了ALO-CV权重与其在平均场推断中的对应权重之间的差异很小。 结合平均场推断估计量与留一输出量之间的上界，这提供了一个证明，表明ALO-CV可以很好地近似留一输出量，误差项可以忽略。 线性模型、平方损失、稳健线性回归和单指数模型被明确处理。 显示英文摘要

摘要： Approximate Leave-One-Out Cross-Validation (ALO-CV) is a method that has been proposed to estimate the generalization error of a regularized estimator in the high-dimensional regime where dimension and sample size are of the same order, the so called ``proportional regime''. A new analysis is developed to derive the consistency of ALO-CV for non-differentiable regularizer under Gaussian covariates and strong-convexity of the regularizer. Using a conditioning argument, the difference between the ALO-CV weights and their counterparts in mean-field inference is shown to be small. Combined with upper bounds between the mean-field inference estimate and the leave-one-out quantity, this provides a proof that ALO-CV approximates the leave-one-out quantity as well up to negligible error terms. Linear models with square loss, robust linear regression and single-index models are explicitly treated.