Amortized Bayesian inference (ABI) with neural networks can solve probabilistic inverse problems orders of magnitude faster than classical methods. However, ABI is not yet sufficiently robust for widespread and safe application. When performing inference on observations outside the scope of the simulated training data, posterior approximations are likely to become highly biased, which cannot be corrected by additional simulations due to the bad pre-asymptotic behavior of current neural posterior estimators. In this paper, we propose a semi-supervised approach that enables training not only on labeled simulated data generated from the model, but also on \textit{unlabeled} data originating from any source, including real data. To achieve this, we leverage Bayesian self-consistency properties that can be transformed into strictly proper losses that do not require knowledge of ground-truth parameters. We test our approach on several real-world case studies, including applications to high-dimensional time-series and image data. Our results show that semi-supervised learning with unlabeled data drastically improves the robustness of ABI in the out-of-simulation regime. Notably, inference remains accurate even when evaluated on observations far away from the labeled and unlabeled data seen during training.

翻译：基于神经网络的摊销贝叶斯推断能以比传统方法快数个数量级的速度解决概率逆问题。然而，ABI 的鲁棒性尚不足以支持其广泛且安全的应用。当对超出模拟训练数据范围的观测进行推断时，后验近似很可能产生高度偏差，而由于当前神经后验估计器的不良渐近前行为，这种偏差无法通过额外的模拟来校正。本文提出一种半监督方法，该方法不仅支持在模型生成的带标签模拟数据上进行训练，也支持在源自任意来源（包括真实数据）的 \textit{无标签} 数据上进行训练。为实现此目标，我们利用贝叶斯自洽性特性，这些特性可转化为严格适当的损失函数，且无需真实参数的知识。我们在多个真实世界案例研究中测试了所提方法，包括对高维时间序列和图像数据的应用。结果表明，利用无标签数据的半监督学习极大地提升了 ABI 在模拟外场景下的鲁棒性。值得注意的是，即使在评估远离训练期间所见带标签及无标签数据的观测时，推断仍能保持准确性。