论文标题
使用仪器变量的稀疏因果效应的可识别性
Identifiability of Sparse Causal Effects using Instrumental Variables
论文作者
论文摘要
例如，外源异质性以仪器变量的形式可以帮助我们学习系统的基本因果结构，并预测看不见的干预实验的结果。在本文中，我们考虑了线性模型，其中$ y $的协变量$ x $的因果效应很少。我们提供因果系数从观察到的分布中可识别的条件。即使乐器数量与因果父母的数量一样小，也可以满足这些条件。我们还制定了图形标准，如果边缘系数是从相对于Lebesgue度量绝对连续的分布中随机采样的，并且$ y $是无子女，则可以在该图形标准下具有概率。作为估计器，我们提出了SpaceIV，并证明如果模型可识别并评估其在模拟数据上的性能，它会始终如一地估计因果效应。如果无法识别性，我们表明仍然有可能恢复因果父母的子集。
Exogenous heterogeneity, for example, in the form of instrumental variables can help us learn a system's underlying causal structure and predict the outcome of unseen intervention experiments. In this paper, we consider linear models in which the causal effect from covariates $X$ on a response $Y$ is sparse. We provide conditions under which the causal coefficient becomes identifiable from the observed distribution. These conditions can be satisfied even if the number of instruments is as small as the number of causal parents. We also develop graphical criteria under which identifiability holds with probability one if the edge coefficients are sampled randomly from a distribution that is absolutely continuous with respect to Lebesgue measure and $Y$ is childless. As an estimator, we propose spaceIV and prove that it consistently estimates the causal effect if the model is identifiable and evaluate its performance on simulated data. If identifiability does not hold, we show that it may still be possible to recover a subset of the causal parents.
