Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables
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含隐藏变量因果图中最优调整集的充要图条件
- 研究问题
- 在存在隐藏变量和条件化变量的因果图中，何时存在最优后门调整集，又如何构造能提高估计效率的调整变量集合？
- 方法与思路
- 作者将最优性表述为调整信息最大化，推导最优调整集存在的充要图条件，并给出定义、构造算法及数值实验。
- 材料陈述的贡献
- 摘要称获得最优集存在的充要判据，并对满足特定信息论方差关系的估计量，将信息最优性转化为最小渐近方差。
- 阅读关注点
- 应区分调整有效性与最优性，核对调整信息的定义、适用估计量类别，以及随机生成图的方式和小样本方差比较。
- 阅读边界
- 所据为 arXiv 预印本，同行评审或期刊接收未经核实；摘要未给出完整图条件，随机图结果不能直接代表现实图的比例。
原文摘要
The problem of selecting optimal backdoor adjustment sets to estimate causal effects in graphical models with hidden and conditioned variables is addressed. Previous work has defined optimality as achieving the smallest asymptotic estimation variance and derived an optimal set for the case without hidden variables. For the case with hidden variables there can be settings where no optimal set exists and currently only a sufficient graphical optimality criterion of limited applicability has been derived. In the present work optimality is characterized as maximizing a certain adjustment information which allows to derive a necessary and sufficient graphical criterion for the existence of an optimal adjustment set and a definition and algorithm to construct it. Further, the optimal set is valid if and only if a valid adjustment set exists and has higher (or equal) adjustment information than the Adjust-set proposed in Perkovi{ć} et al. [Journal of Machine Learning Research, 18: 1--62, 2018] for any graph. The results translate to minimal asymptotic estimation variance for a class of estimators whose asymptotic variance follows a certain information-theoretic relation. Numerical experiments indicate that the asymptotic results also hold for relatively small sample sizes and that the optimal adjustment set or minimized variants thereof often yield better variance also beyond that estimator class. Surprisingly, among the randomly created setups more than 90\% fulfill the optimality conditions indicating that also in many real-world scenarios graphical optimality may hold. Code is available as part of the python package \url{https://github.com/jakobrunge/tigramite}.