We propose a method for inferring the existence of a latent common cause ('confounder') of two observed random variables. The method assumes that the two effects of the confounder are (possibly nonlinear) functions of the confounder plus independent, additive noise. We discuss under which conditions the model is identifiable (up to an arbitrary reparameterization of the confounder) from the joint distribution of the effects. We state and prove a theoretical result that provides evidence for the conjecture that the model is generically identifiable under suitable technical conditions. In addition, we propose a practical method to estimate the confounder from a finite i.i.d. sample of the effects and illustrate that the method works well on both simulated and real-world data.
Partially Linear Additive Gaussian Graphical Models
Princeton University（普林斯顿大学）；Charles H. Dyson School of Applied Economics and Management（查尔斯·H·戴森应用经济与管理学院）；University of Chicago（芝加哥大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Models
University of Chicago（芝加哥大学）；Booth School of Business, University of Chicago（芝加哥大学布斯商学院）；Carnegie Mellon University（卡内基梅隆大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
