用无标签数据提升贝叶斯推断的鲁棒性，避免模型在新数据上严重偏差。
Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data
- 利用贝叶斯自一致性构建无需真值参数的损失函数，实现半监督训练。
- 在高维时间序列与图像数据上，对模拟外数据的推断误差显著降低。
- 适用于真实数据与仿真数据混合场景，适合工业级可靠推断应用。
基于神经网络的变分贝叶斯推断（ABI）可比传统方法快多个数量级，但目前仍缺乏足够鲁棒性。当处理超出训练数据分布的观测时，后验近似易产生严重偏差，且无法通过增加仿真样本修正，因现有神经后验估计器存在预渐近行为不佳问题。本文提出一种半监督方法，可在标注仿真数据外，同时利用任意来源的无标签数据（包括真实数据）进行训练。为此，我们利用贝叶斯自一致性性质，将其转化为严格合理的损失函数，无需依赖真实参数。我们在多个真实案例中测试，涵盖高维时间序列和图像数据。结果表明，引入无标签数据的半监督学习显著提升了ABI在模拟外场景下的鲁棒性，即使在远离训练数据分布的观测上，推断依然准确。
原文摘要 · Abstract (English)
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.
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