Causal intervention is an essential tool in causal inference. It is axiomatized under the rules of do-calculus in the case of structure causal models. We provide simple axiomatizations for families of probability distributions to be different types of interventional distributions. Our axiomatizations neatly lead to a simple and clear theory of causality that has several advantages: it does not need to make use of any modeling assumptions such as those imposed by structural causal models; it only relies on interventions on single variables; it includes most cases with latent variables and causal cycles; and more importantly, it does not assume the existence of an underlying true causal graph as we do not take it as the primitive object--in fact, a causal graph is derived as a by-product of our theory. We show that, under our axiomatizations, the intervened distributions are Markovian to the defined intervened causal graphs, and an observed joint probability distribution is Markovian to the obtained causal graph; these results are consistent with the case of structural causal models, and as a result, the existing theory of causal inference applies. We also show that a large class of natural structural causal models satisfy the theory presented here. We note that the aim of this paper is axiomatization of interventional families, which is subtly different from "causal modeling."
Inverse Probability Weighting-based Mediation Analysis for Microbiome Data
The University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）；The University of Texas MD Anderson Cancer Center（德克萨斯大学安德森癌症中心）；BeOne Medicines（博生医药）；Texas A&M University（德克萨斯农工大学）；University of Toronto（多伦多大学）；Columbia University（哥伦比亚大学）
Learning and Sampling of Atomic Interventions from Observations
National University of Singapore（新加坡国立大学）；Cornell University（康奈尔大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Nebraska-Lincoln（内布拉斯加大学林肯分校）
Data-Driven Influence Functions for Optimization-Based Causal Inference
Department of EECS and Statistics（电气工程与计算机科学系和统计学系）；University of California, Berkeley（加州大学伯克利分校）；Department of Statistics（统计学系）；University of Michigan（密歇根大学）；Department of Data Sciences and Operations（数据科学与运营系）；University of Southern California, Marshall School of Business（南加州大学马歇尔商学院）
