Simulation-based inference methods have been shown to be inaccurate in the data-poor regime, when training simulations are limited or expensive. Under these circumstances, the inference network is particularly prone to overfitting, and using it without accounting for the computational uncertainty arising from the lack of identifiability of the network weights can lead to unreliable results. To address this issue, we propose using Bayesian neural networks in low-budget simulation-based inference, thereby explicitly accounting for the computational uncertainty of the posterior approximation. We design a family of Bayesian neural network priors that are tailored for inference and show that they lead to well-calibrated posteriors on tested benchmarks, even when as few as $O(10)$ simulations are available. This opens up the possibility of performing reliable simulation-based inference using very expensive simulators, as we demonstrate on a problem from the field of cosmology where single simulations are computationally expensive. We show that Bayesian neural networks produce informative and well-calibrated posterior estimates with only a few hundred simulations.

翻译：已有研究表明，在数据匮乏的情况下，当训练模拟受限或成本高昂时，基于模拟的推断方法往往不够准确。在此类场景中，推断网络尤其容易出现过拟合现象，若直接使用该网络而不考虑因网络权重不可识别而产生的计算不确定性，可能导致推断结果不可靠。为解决这一问题，我们提出在低预算模拟推断中采用贝叶斯神经网络，从而显式地处理后验近似带来的计算不确定性。我们设计了一类专为推断任务定制的贝叶斯神经网络先验分布，并证明即使在仅有 $O(10)$ 次模拟的极端条件下，该方法在基准测试中仍能产生校准良好的后验分布。这为使用计算成本极高的模拟器进行可靠的模拟推断提供了可能——我们通过宇宙学领域的一个案例予以验证，该案例中单次模拟的计算开销极大。实验表明，贝叶斯神经网络仅需数百次模拟即可生成信息量充分且校准良好的后验估计。