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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

Portuguese

O objetivo de treinamento do NPE, log-probability, favorece aproximações posteriores que atribuem densidade arbitrariamente alta aos pontos de treinamento, e as famílias típicas de estimadores de densidade condicional amortizados (por exemplo, fluxos normalizantes, codificadores de Gauss) são flexíveis o suficiente para obrigar. A política resultante de superconfiança extrema é mal traduzida para dados mantidos. Parar cedo e outros regularizadores podem prevenir esta degeneração, mas são limitados a selecionar aproximações posteriores ao longo de uma trajetória de otimização desfavorável definida por resíduos de amostra, onde a média posterior é sub-adequada enquanto a variância posterior é excessiva. Para evitar este trade-off, propomos Cross-Fitting NPE (CF-NPE),

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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