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：本文提出了一种针对贝叶斯替代建模和基于模拟的推理中出现的难解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、集合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分布；3）似然网络，用于学习摊销近似似然函数。它们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——这两者是贝叶斯工作流程中的重要组成部分，但通常对于标准方法而言计算成本过高。我们在多种模拟模型上基准测试了JANA的保真度，与最先进的贝叶斯方法进行了比较，并提出了一种用于联合校准的强大且可解释的诊断方法。此外，我们研究了循环似然网络在不依赖手工设计的摘要统计量的情况下模拟复杂时间序列模型的能力。