Data-Driven Influence Functions for Optimization-Based Causal Inference
面向优化型因果推断的数据驱动影响函数AI 解读 ↓
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面向优化型因果推断的数据驱动影响函数
- 研究问题
- 当分布需要从数据估计、目标泛函又由优化问题定义时，如何数值近似影响函数，并保留一步偏差修正的统计性质？
- 方法与思路
- 作者用有限差分近似 Gateaux 导数，比较经验、数值与解析导数，并研究扰动及平滑误差在因果估计和政策优化中的要求。
- 材料陈述的贡献
- 摘要称给出维持一步修正性质的数值近似速率要求，并指出速率双重稳健性可放宽部分要求，但该性质依赖具体目标泛函。
- 阅读关注点
- 应核对扰动和平滑的具体速率、估计分布误差如何进入展开，以及平均潜在结果与无限期马尔可夫决策过程价值的差异。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审及期刊接收未核实；摘要未列出具体速率、正则条件或约束下的证明，不能推断方法普遍适用。
原文摘要
We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing, with a focus on functionals that arise in causal inference. We study the case where probability distributions are not known a priori but need to be estimated from data. These estimated distributions lead to empirical Gateaux derivatives, and we study the relationships between empirical, numerical, and analytical Gateaux derivatives. Starting with a case study of the interventional mean (average potential outcome), we delineate the relationship between finite differences and the analytical Gateaux derivative. We then derive requirements on the rates of numerical approximation in perturbation and smoothing that preserve the statistical benefits of one-step adjustments, such as rate double robustness. We then study more complicated functionals such as dynamic treatment regimes, the linear-programming formulation for policy optimization in infinite-horizon Markov decision processes, and sensitivity analysis in causal inference. More broadly, we study optimization-based estimators, since this begets a class of estimands where identification via regression adjustment is straightforward but obtaining influence functions under minor variations thereof is not. The ability to approximate bias adjustments in the presence of arbitrary constraints illustrates the usefulness of constructive approaches for Gateaux derivatives. We also find that the statistical structure of the functional (rate double robustness) can permit less conservative rates for finite-difference approximation. This property, however, can be specific to particular functionals; e.g., it occurs for the average potential outcome (hence average treatment effect) but not the infinite-horizon MDP policy value.