用鲁棒优化提升小样本下的贝叶斯推断可靠性
Conservative neural posterior estimation via distributionally robust training
- 在Wasserstein模糊集上优化最差情况损失，抑制过拟合
- 在有限模拟下显著降低后验过度自信，提升覆盖率与校准度
- 兼容标准归一化流，适合低模拟预算的科学建模场景
基于模拟的推断中，神经后验估计（NPE）在模拟预算有限时常产生过度自信且不可靠的后验分布。为此，我们提出DRO-NPE，一种基于分布鲁棒优化的方法，将标准NPE目标替换为在Wasserstein模糊集上的最坏情况损失。引入基于KL的误覆盖和校准偏差度量，证明该目标可控制过拟合并减少后验过度自信。方法具有可计算性、可并行化，且可无缝集成至标准归一化流。在基准SBI任务中，DRO-NPE持续改善覆盖率与校准性能，缩小经验与总体NPE损失差距，显著提升小样本条件下的推断可靠性。
原文摘要 · Abstract (English)
Simulation-based inference with neural posterior estimation (NPE) often yields overconfident and unreliable posteriors under limited simulation budgets. To address this, we propose DRO-NPE, a distributionally robust approach that replaces the standard NPE objective with a worst-case loss over a Wasserstein ambiguity set. We introduce KL-based metrics for miscoverage and miscalibration, and use these to show that the DRO-NPE objective controls overfitting and reduces posterior overconfidence. Our method is tractable, parallelisable, and readily integrates with standard normalising flows. Across benchmark SBI tasks, DRO-NPE consistently improves coverage and calibration, while narrowing the gap between empirical and population NPE loss, leading to more reliable inference in low-simulation regimes.
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