We propose a method to improve the efficiency and accuracy of amortized Bayesian inference (ABI) by leveraging universal symmetries in the probabilistic joint model $p(\theta, y)$ of parameters $\theta$ and data $y$. In a nutshell, we invert Bayes' theorem and estimate the marginal likelihood based on approximate representations of the joint model. Upon perfect approximation, the marginal likelihood is constant across all parameter values by definition. However, approximation error leads to undesirable variance in the marginal likelihood estimates across different parameter values. We formulate violations of this symmetry as a loss function to accelerate the learning dynamics of conditional neural density estimators. We apply our method to a bimodal toy problem with an explicit likelihood (likelihood-based) and a realistic model with an implicit likelihood (simulation-based).

翻译：我们提出一种方法，通过利用参数θ和数据y的概率联合模型p(θ, y)中的普适对称性，来提高自洽贝叶斯推断（ABI）的效率和准确性。简言之，我们反向运用贝叶斯定理，基于联合模型的近似表示来估计边际似然。在完美近似条件下，边际似然根据定义在所有参数值上保持恒定。然而，近似误差会导致不同参数值下的边际似然估计出现不期望的方差。我们将这种对称性的违反构建为损失函数，以加速条件神经密度估计器的学习动态。我们将该方法应用于一个具有显式似然（基于似然）的双峰玩具问题，以及一个具有隐式似然（基于模拟）的现实模型。