提出最小规范扰动，量化因果推断中多大改动会导致结论失效
Minimum Specification Perturbation: Robustness as Distance-to-Falsification in Causal Inference
- 定义最小规范扰动（MSP），衡量使结果失效所需的最少分析决策变动数
- 在LaLonde数据集上，仅需1次改动就让置信区间包含零，揭示结果脆弱性
- 适合关注因果推断稳健性的研究者，尤其适用于弱效应场景
实证因果推断依赖大量分析者决策，如协变量选择和估计器使用。现有稳健性工具仅描述结果随决策变化的波动，但未回答：要改变多少个分析决策，才能得到一个包含零的置信区间？本文提出最小规范扰动（MSP），即导致结论失效的最小决策变更数。在原假设下MSP较小，效应越强则MSP越大，能捕捉到传统方差度量无法反映的“距离失效”信息。在弱效应下，基于MSP的决策规则比基于方差的规则具有更低的假阳性率。我们证明脆弱性指数与MSP衡量的是正交的脆弱性：对异常值敏感不等于对规范选择敏感。在LaLonde基准数据集上，MSP=1意味着只需一次决策变化即可使置信区间包含零。我们还提供了随机化下的精确置换校准，并刻画了计算复杂性：在可加结构下可计算，一般情况下为NP难。
原文摘要 · Abstract (English)
Empirical causal claims depend on many analyst decisions, from selecting covariates to choosing estimators. Existing robustness tools summarize how results vary across these choices, but, to the best of our knowledge, do not answer: \textbf{How many analyst decisions must change to reach a specification, which is a set of choices, whose confidence interval (CI) contains zero?} We introduce \emph{Minimum Specification Perturbation (MSP)}, the smallest number of changes. MSP is small under the null, grows with effect strength and captures distance-to-falsification information that dispersion-based summaries cannot report; when making decisions under weak effects, an MSP-based rule yields lower false-positive rates than dispersion-based rules. We show that Fragility Index and MSP measure orthogonal vulnerabilities: fragility to influential observations need not imply fragility to specification choices. On the LaLonde benchmark, MSP = 1 implies that one decision change makes the CI contain zero. We further provide exact permutation calibration under randomization and characterize computation, showing tractable cases under additive structure and NP-hardness in general.
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