Post-selection inference for causal effects after causal discovery
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因果发现后的因果效应选择后推断
- 研究问题
- 同一数据先用于发现因果图再估计处理效应时，如何处理模型选择与图误选，使置信集合覆盖固定的真实因果参数？
- 方法与思路
- 作者通过重抽样和筛选随机改变中间检验统计量，多次执行因果发现，再将各图对应的效应估计和区间合并构造置信集合。
- 材料陈述的贡献
- 摘要称该构造对固定总体因果效应具有渐近正确覆盖率，并以 PC 算法和多元高斯情形阐述可扩展的模块化方法。
- 阅读关注点
- 应核对因果图识别和条件独立检验的要求、筛选保留有效图的条件，以及区间并集的宽度、计算成本与覆盖率证明。
- 阅读边界
- 所给版本为 arXiv 预印本，不能据此确认同行评审或期刊接收；摘要未列出覆盖保证的完整条件，不能视为任意因果发现都有效。
原文摘要
Algorithms for constraint-based causal discovery select graphical causal models among a space of possible candidates (e.g., all directed acyclic graphs) by executing a sequence of conditional independence tests. These may be used to inform the estimation of causal effects (e.g., average treatment effects) when there is uncertainty about which covariates ought to be adjusted for, or which variables act as confounders versus mediators. However, naively using the data twice, for model selection and estimation, would lead to invalid confidence intervals. Moreover, if the selected graph is incorrect, the inferential claims may apply to a selected functional that is distinct from the actual causal effect. We propose an approach to post-selection inference that is based on a resampling and screening procedure, which essentially performs causal discovery multiple times with randomly varying intermediate test statistics. Then, an estimate of the target causal effect and corresponding confidence sets are constructed from a union of individual graph-based estimates and intervals. We show that this construction has asymptotically correct coverage for the true causal effect parameter. Importantly, the guarantee holds for a fixed population-level effect, not a data-dependent or selection-dependent quantity. Most of our exposition focuses on the PC-algorithm for learning directed acyclic graphs and the multivariate Gaussian case for simplicity, but the approach is general and modular, so it may be used with other conditional independence based discovery algorithms and distributional families.