This work proposes ``jointly amortized neural approximation'' (JANA) of intractable likelihood functions and posterior densities arising in Bayesian surrogate modeling and simulation-based inference. We train three complementary networks in an end-to-end fashion: 1) a summary network to compress individual data points, sets, or time series into informative embedding vectors; 2) a posterior network to learn an amortized approximate posterior; and 3) a likelihood network to learn an amortized approximate likelihood. Their interaction opens a new route to amortized marginal likelihood and posterior predictive estimation -- two important ingredients of Bayesian workflows that are often too expensive for standard methods. We benchmark the fidelity of JANA on a variety of simulation models against state-of-the-art Bayesian methods and propose a powerful and interpretable diagnostic for joint calibration. In addition, we investigate the ability of recurrent likelihood networks to emulate complex time series models without resorting to hand-crafted summary statistics.

翻译：本文提出了一种用于贝叶斯替代建模和基于模拟的推断中难以处理的似然函数和后验密度的“联合摊销神经逼近”（JANA）方法。我们以端到端方式训练三个互补网络：1) 摘要网络，用于将单个数据点、数据集或时间序列压缩为信息性嵌入向量；2) 后验网络，用于学习摊销近似后验；3) 似然网络，用于学习摊销近似似然。三者的相互作用为摊销边际似然和后验预测估计开辟了新途径——这两个贝叶斯工作流中的重要组成部分通常因标准方法成本过高而难以实现。我们针对多种模拟模型，将JANA的保真度与最先进的贝叶斯方法进行基准测试，并提出了一种强大且可解释的联合校准诊断工具。此外，我们研究了循环似然网络在不依赖人工设计摘要统计量的情况下模拟复杂时间序列模型的能力。