Neural amortized Bayesian inference (ABI) can solve probabilistic inverse problems orders of magnitude faster than classical methods. However, neural ABI is not yet sufficiently robust for widespread and safe applicability. In particular, when performing inference on observations outside of the scope of the simulated data seen during training, for example, because of model misspecification, the posterior approximations are likely to become highly biased. Due to the bad pre-asymptotic behavior of current neural posterior estimators in the out-of-simulation regime, the resulting estimation biases cannot be fixed in acceptable time by just simulating more training data. In this proof-of-concept paper, we propose a semi-supervised approach that enables training not only on (labeled) simulated data generated from the model, but also on unlabeled data originating from any source, including real-world data. To achieve the latter, we exploit Bayesian self-consistency properties that can be transformed into strictly proper losses without requiring knowledge of true parameter values, that is, without requiring data labels. The results of our initial experiments show remarkable improvements in the robustness of ABI on out-of-simulation data. Even if the observed data is far away from both labeled and unlabeled training data, inference remains highly accurate. If our findings also generalize to other scenarios and model classes, we believe that our new method represents a major breakthrough in neural ABI.

翻译：神经摊销贝叶斯推断（ABI）能够以比传统方法快数个数量级的速度解决概率逆问题。然而，神经ABI目前尚未达到足够鲁棒的程度，以实现广泛且安全的应用。具体而言，当对超出训练期间所见模拟数据范围的观测值进行推断时（例如由于模型设定错误），后验近似很可能产生严重偏差。由于当前神经后验估计器在模拟范围之外表现出较差的前渐近行为，仅通过模拟更多训练数据无法在可接受的时间内修正由此产生的估计偏差。在这篇概念验证论文中，我们提出了一种半监督方法，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，还能利用来自任何来源（包括真实世界数据）的无标签数据进行训练。为实现后者，我们利用了贝叶斯自洽性特性，这些特性可转化为严格适当的损失函数，且无需知晓真实参数值，即无需数据标签。我们的初步实验结果表明，该方法在模拟范围之外数据上的ABI鲁棒性取得了显著提升。即使观测数据远离带标签和无标签的训练数据，推断仍能保持高度准确性。如果我们的发现也能推广到其他场景和模型类别，我们相信这一新方法代表了神经ABI领域的一项重大突破。