首次揭示神经后验与似然估计的统计精度，证明其比传统方法更高效。
The Statistical Accuracy of Neural Posterior and Likelihood Estimation
- 基于理论分析，建立神经后验/似然估计与经典方法的等价性
- 在相同精度下，计算成本远低于ABC和BSL方法
- 适合需要高效贝叶斯推断的复杂建模场景
神经后验估计（NPE）和神经似然估计（NLE）是机器学习方法，在复杂建模中提供准确的后验与似然近似，尤其适用于需摊销推断的情形。尽管这些方法在多个科学领域展现出显著潜力，其统计准确性此前未被深入探讨。本文首次系统研究了NPE与NLE的统计行为，证明其理论保证与常见统计方法（如近似贝叶斯计算（ABC）和贝叶斯合成似然（BSL））相当。虽然NPE与NLE的精度与ABC、BSL相当，但通常可在大幅降低计算成本的情况下实现，因此在某些问题中可提供更具吸引力的近似方案。我们通过理论验证和文献中的多个实例确认了上述结论。
原文摘要 · Abstract (English)
Neural posterior estimation (NPE) and neural likelihood estimation (NLE) are machine learning approaches that provide accurate posterior, and likelihood, approximations in complex modeling scenarios, and in situations where conducting amortized inference is a necessity. While such methods have shown significant promise across a range of diverse scientific applications, the statistical accuracy of these methods is so far unexplored. In this manuscript, we give, for the first time, an in-depth exploration on the statistical behavior of NPE and NLE. We prove that these methods have similar theoretical guarantees to common statistical methods like approximate Bayesian computation (ABC) and Bayesian synthetic likelihood (BSL). While NPE and NLE methods are just as accurate as ABC and BSL, we prove that this accuracy can often be achieved at a vastly reduced computational cost, and will therefore deliver more attractive approximations than ABC and BSL in certain problems. We verify our results theoretically and in several examples from the literature.
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