In many observational studies, researchers are often interested in studying the effects of multiple exposures on a single outcome. Standard approaches for high-dimensional data such as the lasso assume the associations between the exposures and the outcome are sparse. These methods, however, do not estimate the causal effects in the presence of unmeasured confounding. In this paper, we consider an alternative approach that assumes the causal effects in view are sparse. We show that with sparse causation, the causal effects are identifiable even with unmeasured confounding. At the core of our proposal is a novel device, called the synthetic instrument, that in contrast to standard instrumental variables, can be constructed using the observed exposures directly. We show that under linear structural equation models, the problem of causal effect estimation can be formulated as an $\ell_0$-penalization problem, and hence can be solved efficiently using off-the-shelf software. Simulations show that our approach outperforms state-of-art methods in both low-dimensional and high-dimensional settings. We further illustrate our method using a mouse obesity dataset.

翻译：在许多观察性研究中，研究者通常关注多种暴露对单一结局的影响。针对高维数据的标准方法（如Lasso）假设暴露与结局之间的关联是稀疏的。然而，这些方法在存在未测量混杂因素时无法估计因果效应。本文考虑一种替代方法，假设所关注的因果效应是稀疏的。我们证明，在稀疏因果假设下，即使存在未测量混杂因素，因果效应也是可识别的。该方法的核心理念是一个新型工具——称为合成工具变量——与标准工具变量不同，它可直接利用观测到的暴露构建。我们表明，在线性结构方程模型下，因果效应估计问题可转化为ℓ₀惩罚问题，进而可利用现成软件高效求解。模拟实验显示，我们的方法在低维和高维场景中均优于现有最优方法。我们进一步使用小鼠肥胖数据集验证了该方法。