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

Pierre C Bellec

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arXiv · 2501.02624

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

Pierre C Bellec

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Abstract

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 regularizers under Gaussian covariates and strong convexity. 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 up to negligible error terms. Linear models with square loss, robust linear regression and single-index models are explicitly treated.

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BibTeX RIS

Pierre C Bellec. 2026-02-12. Simultaneous analysis of approximate leave-one-out cross-validation and mean-field inference. https://arxiv.org/abs/2501.02624

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