Simulation-based inference (SBI) enables amortized Bayesian inference by first training a neural posterior estimator (NPE) on prior-simulator pairs, typically through low-dimensional summary statistics, which can then be cheaply reused for fast inference by querying it on new test observations. Because NPE is estimated under the training data distribution, it is susceptible to misspecification when observations deviate from the training distribution. Many robust SBI approaches address this by modifying NPE training or introducing error models, coupling robustness to the inference network and compromising amortization and modularity. We introduce minimum-distance summaries, a plug-in robust NPE method that adapts queried test-time summaries independently of the pretrained NPE. Leveraging the maximum mean discrepancy (MMD) as a distance between observed data and a summary-conditional predictive distribution, the adapted summary inherits strong robustness properties from the MMD. We demonstrate that the algorithm can be implemented efficiently with random Fourier feature approximations, yielding a lightweight, model-free test-time adaptation procedure. We provide theoretical guarantees for the robustness of our algorithm and empirically evaluate it on a range of synthetic and real-world tasks, demonstrating substantial robustness gains with minimal additional overhead.

翻译：基于模拟的推断（SBI）通过首先在先验-模拟器对（通常通过低维摘要统计量）上训练神经后验估计器（NPE），实现摊销式贝叶斯推断；随后，通过在新测试观测上查询该估计器，即可廉价地重复用于快速推断。由于NPE是在训练数据分布下估计的，当观测偏离训练分布时，其易受模型设定错误的影响。许多鲁棒SBI方法通过修改NPE训练或引入误差模型来解决此问题，但这将鲁棒性与推断网络耦合，损害了摊销性和模块化。我们提出最小距离摘要，这是一种即插即用的鲁棒NPE方法，可在不依赖预训练NPE的情况下，独立地调整查询时的测试摘要。该方法利用最大平均差异（MMD）作为观测数据与摘要条件预测分布之间的距离，使调整后的摘要继承了MMD的强大鲁棒特性。我们证明该算法可通过随机傅里叶特征近似高效实现，从而形成一个轻量级、无模型的测试时自适应过程。我们为算法的鲁棒性提供了理论保证，并在一系列合成及现实任务上进行了实证评估，结果表明该方法能以极小的额外开销实现显著的鲁棒性提升。