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arXiv 0810.4214stat.ME
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从观测数据估计高维干预效应

Estimating high-dimensional intervention effects from observational data

Marloes H. Maathuis, Markus Kalisch, Peter Bühlmann

摘要:

我们假设我们有从未知的底层有向无环图(DAG)模型生成的观测数据。DAG通常无法从观测数据中识别,但可以一致地估计DAG的等价类。此外,对于任何给定的DAG,因果效应可以使用干预演算来估计。在本文中,我们将这两个部分结合起来。对于估计等价类中的每个DAG,我们使用干预演算来估计协变量对响应的因果效应。这产生了每个协变量的估计因果效应的集合。我们表明,在这个集合中的独特的值可以一致地估计的算法,只使用局部信息的图。这种局部方法在高维问题中计算速度快且可行。我们建议使用一组可能的因果效应的汇总措施,以确定变量的重要性。特别是,我们使用这个集合的最小绝对值,因为这是因果效应大小的下限。我们证明了我们的方法在模拟研究和核黄素生产的数据集的优点。

英文摘要:

We assume that we have observational data generated from an unknown underlying directed acyclic graph (DAG) model. A DAG is typically not identifiable from observational data, but it is possible to consistently estimate the equivalence class of a DAG. Moreover, for any given DAG, causal effects can be estimated using intervention calculus. In this paper, we combine these two parts. For each DAG in the estimated equivalence class, we use intervention calculus to estimate the causal effects of the covariates on the response. This yields a collection of estimated causal effects for each covariate. We show that the distinct values in this set can be consistently estimated by an algorithm that uses only local information of the graph. This local approach is computationally fast and feasible in high-dimensional problems. We propose to use summary measures of the set of possible causal effects to determine variable importance. In particular, we use the minimum absolute value of this set, since that is a lower bound on the size of the causal effect. We demonstrate the merits of our methods in a simulation study and on a data set about riboflavin production.

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