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“联合摊销神经逼近”（JANA），用于处理贝叶斯替代建模与基于模拟的推断中难以处理的似然函数和后验密度。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。三者的交互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中的关键要素，但传统方法往往因计算成本过高而难以处理。我们在一系列模拟模型上，针对最新贝叶斯方法基准评估了JANA的保真度，并提出一种强大且可解释的联合校准诊断方法。此外，我们研究了递归似然网络在不依赖手工摘要统计量的情况下模拟复杂时间序列模型的能力。