In Simulation-based Inference, the goal is to solve the inverse problem when the likelihood is only known implicitly. Neural Posterior Estimation commonly fits a normalized density estimator as a surrogate model for the posterior. This formulation cannot easily fit unnormalized surrogates because it optimizes the Kullback-Leibler divergence. We propose to optimize a generalized Kullback-Leibler divergence that accounts for the normalization constant in unnormalized distributions. The objective recovers Neural Posterior Estimation when the model class is normalized and unifies it with Neural Ratio Estimation, combining both into a single objective. We investigate a hybrid model that offers the best of both worlds by learning a normalized base distribution and a learned ratio. We also present benchmark results.

翻译：在基于仿真的推断中，目标是在似然仅隐含已知的情况下求解逆问题。神经后验估计通常将归一化密度估计器拟合为后验的替代模型。这一框架因优化KL散度而难以拟合未归一化的替代模型。我们提出优化一种广义KL散度，该散度考虑了未归一化分布中的归一化常数。当模型类别为归一化时，该目标函数恢复神经后验估计，并将其与神经比率估计统一起来，将两者结合为单一目标。我们研究了一种混合模型，通过学习归一化的基分布与可学习的比率，实现了两者的最优结合。同时给出了基准测试结果。