Axiomatization of Interventional Probability Distributions
干预概率分布的公理化AI 解读 ↓
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干预概率分布的公理化
- 研究问题
- 研究如何直接对概率分布族给出干预分布的公理刻画，在不以预先存在的因果图为基本对象时建立因果理论。
- 方法与思路
- 作者以单变量干预为基础提出公理体系，从分布族导出因果图，并分析观测和干预分布相对所得图的马尔可夫性质。
- 材料陈述的贡献
- 摘要称，该框架涵盖多数潜变量与因果循环情形，与结构因果模型的相关结果相容，并证明一大类结构因果模型满足所提理论。
- 阅读关注点
- 应核对各条公理的实质限制、潜变量与循环的适用范围，以及由分布导出图的步骤和公理化与因果建模之间的区别。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实；摘要未列出公理，不能将无需结构模型假设理解为因果推断完全无需限制。
原文摘要
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."