Neural networks have recently shown promise for likelihood-free inference, providing orders-of-magnitude speed-ups over classical methods. However, current implementations are suboptimal when estimating parameters from independent replicates. In this paper, we use a decision-theoretic framework to argue that permutation-invariant neural networks are ideally placed for constructing Bayes estimators for arbitrary models, provided that simulation from these models is straightforward. We show that the resulting neural Bayes estimators can quickly and optimally estimate parameters in weakly-identified and highly-parameterised models with relative ease, and that they are highly competitive and much faster than traditional likelihood-based estimators. We apply our estimator on a spatial analysis of sea-surface temperature in the Red Sea where, after training, we obtain parameter estimates, and uncertainty quantification of the estimates via bootstrap sampling, from hundreds of spatial fields in a fraction of a second.

翻译：神经网络近期在无似然推断领域展现潜力，相较于传统方法可实现数量级加速。然而，当前实现在对独立重复样本进行参数估计时仍非最优。本文采用决策理论框架论证，在模型模拟可行前提下，置换不变神经网络是构建任意模型贝叶斯估计量的理想工具。研究表明，此类神经贝叶斯估计量能快速、最优地估计弱识别和高参数化模型中的参数，且与传统基于似然的估计量相比更具竞争力和显著的速度优势。我们将该估计量应用于红海海表温度空间分析：在完成训练后，通过自助采样对数百个空间场进行参数估计与不确定性量化，整个过程仅需不到一秒钟。