We present an algorithm for estimating bounds on causal effects from observational data which combines graphical model search with simple linear regression. We assume that the underlying system can be represented by a linear structural equation model with no feedback, and we allow for the possibility of latent confounders. Under assumptions standard in the causal search literature, we use conditional independence constraints to search for an equivalence class of ancestral graphs. Then, for each model in the equivalence class, we perform the appropriate regression (using causal structure information to determine which covariates to adjust for) to estimate a set of possible causal effects. Our approach is based on the IDA procedure of Maathuis et al. (2009), which assumes that all relevant variables have been measured (i.e., no latent confounders). We generalize their work by relaxing this assumption, which is often violated in applied contexts. We validate the performance of our algorithm in simulation experiments.

中文翻译：

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估计高维和可能混杂系统中因果效应的界限


我们提出了一种根据观测数据估计因果效应界限的算法，该算法将图形模型搜索与简单线性回归相结合。我们假设底层系统可以用没有反馈的线性结构方程模型来表示，并且我们考虑到潜在混杂因素的可能性。根据因果搜索文献中的假设标准，我们使用条件独立约束来搜索祖先图的等价类。然后，对于等价类中的每个模型，我们执行适当的回归（使用因果结构信息来确定要调整哪些协变量）以估计一组可能的因果效应。我们的方法基于 Maathuis 等人的 IDA 程序。 （2009），假设所有相关变量都已测量（即没有潜在的混杂因素）。我们通过放宽这一假设来概括他们的工作，该假设在应用环境中经常被违反。我们在模拟实验中验证了算法的性能。