用最小距离摘要提升神经后验估计的鲁棒性,测试时无需重训练。
Minimum Distance Summaries for Robust Neural Posterior Estimation
- 引入最小距离摘要,测试时独立调整摘要以增强鲁棒性。
- 基于MMD度量偏差,实测在合成与真实数据上显著提升鲁棒性。
- 轻量级无模型方法,适合对泛化能力有要求的贝叶斯推断场景。
基于模拟的推断(SBI)通过先在先验-模拟器对上训练神经后验估计器(NPE),利用低维摘要统计量实现可复用的贝叶斯推断,从而快速处理新观测。由于NPE在训练数据分布下估计,当观测偏离训练分布时易出现误设。现有鲁棒SBI方法常修改NPE训练或引入误差模型,牺牲了摊销优势与模块性。本文提出最小距离摘要,一种可即插即用的鲁棒NPE方法,能在测试时独立调整查询摘要,不依赖预训练NPE。利用最大均值差异(MMD)衡量观测数据与摘要条件预测分布间的距离,所获摘要继承强鲁棒性。算法可通过随机傅里叶特征近似高效实现,形成轻量、无模型的测试时自适应流程。我们提供理论保证,并在多种合成与真实任务中验证其性能,结果显示在极小额外开销下获得显著鲁棒性提升。
原文摘要 · Abstract (English)
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.
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