提出CoLT测试,精准定位神经后验的误差区域。
CoLT: The conditional localization test for assessing the accuracy of neural posterior estimates

- 通过自适应选择偏差点,高效检测后验差异。
- 仅需每样本一个真后验采样,却能发现显著偏差。
- 适合模拟推断场景,可指导模型优化。
针对神经后验估计 $ q(θ ext{∣}x) $ 是否准确逼近真实后验 $ p(θ ext{∣}x) $ 的验证问题,本文提出条件定位测试(CoLT)。现有方法多依赖分类器测试或散度度量,存在实际局限。CoLT通过学习一个定位函数,自适应选取在每个 $ x $ 处 $ q $ 与 $ p $ 差异最大的 $ θ_l(x) $,无需对所有 $ x $ 进行密集比较或密度估计。该方法特别适用于模拟推断场景:每 $ x $ 仅有一个真实后验样本 $ θ ext{∼}p(θ ext{∣}x) $,但可任意采样 $ q(θ ext{∣}x) $。理论证明了分布等价性所需的充要条件,兼具严格保证与可扩展性。实验表明,CoLT在对比 $ p $ 与 $ q $ 时表现更优,并能精确定位显著偏差区域,为模型改进提供可操作洞察。因此,CoLT是当前最先进的神经后验验证方法。
原文摘要 · Abstract (English)
We consider the problem of validating whether a neural posterior estimate \( q(θ\mid x) \) is an accurate approximation to the true, unknown true posterior \( p(θ\mid x) \). Existing methods for evaluating the quality of an NPE estimate are largely derived from classifier-based tests or divergence measures, but these suffer from several practical drawbacks. As an alternative, we introduce the \emph{Conditional Localization Test} (CoLT), a principled method designed to detect discrepancies between \( p(θ\mid x) \) and \( q(θ\mid x) \) across the full range of conditioning inputs. Rather than relying on exhaustive comparisons or density estimation at every \( x \), CoLT learns a localization function that adaptively selects points $θ_l(x)$ where the neural posterior $q$ deviates most strongly from the true posterior $p$ for that $x$. This approach is particularly advantageous in typical simulation-based inference settings, where only a single draw \( θ\sim p(θ\mid x) \) from the true posterior is observed for each conditioning input, but where the neural posterior \( q(θ\mid x) \) can be sampled an arbitrary number of times. Our theoretical results establish necessary and sufficient conditions for assessing distributional equality across all \( x \), offering both rigorous guarantees and practical scalability. Empirically, we demonstrate that CoLT not only performs better than existing methods at comparing $p$ and $q$, but also pinpoints regions of significant divergence, providing actionable insights for model refinement. These properties position CoLT as a state-of-the-art solution for validating neural posterior estimates.
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