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Cross-Fitting for Neural Posterior Estimation

Jeffrey Regier · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26733 · cited by 0 works (OpenAlex) · open-access PDF

French

L'estimation postérieure neuronale (NPE) correspond à un estimateur de densité conditionnelle amortisée à un ensemble de réalisations de données complètes simulées. L'objectif de formation de NPE, log-probabilité, favorise les approximations postérieures qui attribuent des densités arbitraires élevées aux points de formation, et les familles typiques d'estimateurs de densité conditionnelle amortisés (par exemple, normalisant les flux, codage gaussien) sont suffisamment flexibles pour obliger. La politique résultante de surconfiance extrême se traduit mal par des données détenues. L'arrêt précoce et d'autres régularisateurs peuvent empêcher cette dégénérescence, mais ils sont limités à sélectionner des approximations postérieures

Machine translation (Meta M2M100); the English original follows.

Abstract

Neural Posterior Estimation (NPE) fits an amortized conditional density estimator to a simulated training set of complete-data realizations. NPE's training objective, log-likelihood, favors posterior approximations that assign arbitrarily high density to the training points, and typical families of amortized conditional density estimators (e.g., normalizing flows, Gaussian encoders) are flexible enough to oblige. The resulting policy of extreme overconfidence translates poorly to held-out data. Early stopping and other regularizers can prevent this degeneracy, but they are limited to selecting posterior approximations along an unfavorable optimization trajectory set by in-sample residuals, where the posterior mean is underfit while the posterior variance is overfit. To avoid this trade-off, we propose Cross-Fitting NPE (CF-NPE), which uses sample splitting to separate conditional-mean estimation from the estimation of the posterior's higher moments. Using $K$-fold cross-fitting, CF-NPE fits $K$ posterior-mean regressors and then fits a conditional density estimator to the resulting out-of-fold residuals. In experiments with synthetic data and in a cosmological application, CF-NPE achieves higher held-out log-likelihood than standard NPE and typically improves calibration. CF-NPE is most useful in high-dimensional, simulation-limited settings.

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Topics: Estimator, Mathematics, Density estimation, Algorithm, Gaussian, Set (abstract data type)

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