Estimating Causal Direction and Confounding Of Two Discrete Variables
Krzysztof Chalupka Computation and Neural Systems Caltech、Frederick Eberhardt Humanities and Social Sciences Caltech、Pietro Perona Electrical Engineering Caltech
Abstract
We propose a method to classify the causal relationship between two discrete variables given only the joint distribution of the variables, acknowledging that the method is subject to an inherent baseline error. We assume that the causal system is acyclicity, but we do allow for hidden common causes. Our algorithm presupposes that the probability distributions $P(C)$ of a cause $C$ is independent from the probability distribution $P(E\mid C)$ of the cause-effect mechanism. While our classifier is trained with a Bayesian assumption of flat hyperpriors, we do not make this assumption about our test data. This work connects to recent developments on the identifiability of causal models over continuous variables under the assumption of ”independent mechanisms”. Carefully-commented Python notebooks that reproduce all our experiments are available online at vision.caltech.edu/~kchalupk/code.html.
中文速览
判断两个离散变量之间的因果方向（causal direction），在没有实验干预的情况下，是一个在理论上无法完全识别的难题。本文提出一种基于贝叶斯假设的算法：核心思想是"独立机制（independent mechanisms）"——即原因的边际分布与"原因→结果"的条件分布相互独立，并对两者分别赋予无信息的狄利克雷先验（Dirichlet prior），从而计算六种可能因果结构（纯因果、纯混淆、因果加混淆等）各自的似然比，进而做出分类判断。理论推导给出了一个解析形式的似然比分类器（LR classifier），并通过蒙特卡洛实验估计了其在不同变量基数下的基线误差——变量取值越多，分类准确率越高，例如变量各取10个状态时误差已低于0.1%。这项工作的重要意义在于，它是首个无需干预、无需加性噪声等强函数假设、同时能区分"直接因果"与"隐藏共因混淆"六类结构的离散变量因果推断方法，为观测数据驱动的因果发现提供了新的理论基础。
原文 arXiv:1611.01504;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1611.01504v1