论文标题
神经经验贝叶斯：源分布估计及其在基于仿真推理中的应用
Neural Empirical Bayes: Source Distribution Estimation and its Applications to Simulation-Based Inference
论文作者
论文摘要
我们在没有可进行的可能性功能的情况下重新审视经验贝叶斯，这是依靠计算机模拟的科学领域中的典型情况。我们研究了经验贝叶斯如何首先利用神经密度估计器使用所有噪声浪费的观测值来估计未腐败的样品对先前或源分布，然后使用拟合源分布进行单观观测后推理。我们提出了一种基于观测值的对数 - 边界可能性的直接最大化，检查偏见和偏置估计器的方法，并与变分方法进行比较。我们发现，为对称性，一种神经经验贝叶斯方法恢复了地面真实源分布。借助手头的源分布，我们显示了无可能推断的适用性，并检查了所得后验估计的质量。最后，我们证明了神经经验贝叶斯对撞机物理学的反问题的适用性。
We revisit empirical Bayes in the absence of a tractable likelihood function, as is typical in scientific domains relying on computer simulations. We investigate how the empirical Bayesian can make use of neural density estimators first to use all noise-corrupted observations to estimate a prior or source distribution over uncorrupted samples, and then to perform single-observation posterior inference using the fitted source distribution. We propose an approach based on the direct maximization of the log-marginal likelihood of the observations, examining both biased and de-biased estimators, and comparing to variational approaches. We find that, up to symmetries, a neural empirical Bayes approach recovers ground truth source distributions. With the learned source distribution in hand, we show the applicability to likelihood-free inference and examine the quality of the resulting posterior estimates. Finally, we demonstrate the applicability of Neural Empirical Bayes on an inverse problem from collider physics.
