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，研究者常关注多个暴露变量对单一结局的影响。针对高维数据的标准方法（如lasso）通常假设暴露变量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。本文提出一种替代性方法，其假设所考察的因果效应本身具有稀疏性。我们证明在稀疏因果性假设下，即使存在未测量混杂，因果效应仍可被识别。本方法的核心是一种称为“合成工具”的新型工具变量装置——与标准工具变量不同，该工具可直接利用观测到的暴露变量构建。在线性结构方程模型框架下，我们将因果效应估计问题转化为$\ell_0$惩罚优化问题，从而可利用现成软件高效求解。模拟实验表明，本方法在低维与高维场景下均优于当前主流方法。我们进一步通过小鼠肥胖数据集展示了该方法的应用。