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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

Japanese

NPEのトレーニング目標、log-probabilityは、トレーニングポイントに任意に高密度を割り当てたデータのアプローチを好み、およびアプローチされた条件密度のアプローチの典型的な家族(例えば、正常化フロー、ガウシアンエンコード)は、サンプル残留物によって設定された不利な最適化軌道に沿って後方アプローチを選択するのに十分に柔軟である。極端な過剰信頼性の結果のポリシーは過剰信頼性に悪く翻訳されます。 早期停止および他の規則化剤は、この退化を防ぐことができますが、サンプルシミュレーションは、標準的な高密度の推定値を分離するためにサンプルシミュレーションによって設定

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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