In causal inference, it is common to estimate the causal effect of a single treatment variable on an outcome. However, practitioners may also be interested in the effect of simultaneous interventions on multiple covariates of a fixed target variable. We propose a novel method that allows to estimate the effect of joint interventions using data from different experiments in which only very few variables are manipulated. If there is only little randomized data or no randomized data at all, one can use observational data sets if certain parental sets are known or instrumental variables are available. If the joint causal effect is linear, the proposed method can be used for estimation and inference of joint causal effects, and we characterize conditions for identifiability. In the overidentified case, we indicate how to leverage all the available causal information across multiple data sets to efficiently estimate the causal effects. If the dimension of the covariate vector is large, we may only have a few samples in each data set. Under a sparsity assumption, we derive an estimator of the causal effects in this high-dimensional scenario. In addition, we show how to deal with the case where a lack of experimental constraints prevents direct estimation of the causal effects. When the joint causal effects are non-linear, we characterize conditions under which identifiability holds, and propose a non-linear causal aggregation methodology for experimental data sets similar to the gradient boosting algorithm where in each iteration we combine weak learners trained on different datasets using only unconfounded samples. We demonstrate the effectiveness of the proposed method on simulated and semi-synthetic data.
Causal Data Fusion for Panel Data without a Pre-Intervention Period
Faculty of Computing and Data Sciences, Boston University（波士顿大学计算与数据科学学院）；Division of Infectious Diseases, Boston Children’s Hospital & Harvard Medical School（波士顿儿童医院感染病科及哈佛医学院）；Department of Mathematics and Statistics, Boston University（波士顿大学数学与统计系）
Stable Causal Discovery via Directed Acyclic Graph Aggregation
Yau Mathematical Sciences Center, Tsinghua University（丘成桐数学科学中心，清华大学）；Department of Statistics, University of Virginia（弗吉尼亚大学统计系）；Dr. Bing Zhang Department of Statistics, University of Kentucky（肯塔基大学张炳章统计系）
Department of Computer Science and Engineering, Hanyang University（韩阳大学计算机科学与工程系）；Department of Applied Artificial Intelligence, Hanyang University（韩阳大学应用人工智能系）
Causal Discovery Should Embrace the Wisdom of the Crowd
Department of Industrial and Systems Engineering, University of Washington（华盛顿大学工业与系统工程系）；Department of Applied Mathematics, Illinois Institute of Technology（伊利诺伊理工学院应用数学系）；Department of Electrical & Computer Engineering, Texas A&M University（德克萨斯阿灵顿大学电气与计算机工程系）
Models and Algorithms for Data and Text Mining Laboratory (MADLab) Department of Informatics Systems and Communication (DISCo) University of Milano - Bicocca Milan Italy（数据与文本挖掘算法实验室（MADLab）信息系统与通信系（DISCo）米兰-比科卡大学）；Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA) Lugano Switzerland（智能研究 institute（IDSIA）卢加诺瑞士）；University of Milano - Bicocca Milan Italy（米兰-比科卡大学）
