标题： 边缘化DAG中的不等式约束的图形方法 显示英文标题

标题： Graphical methods for inequality constraints in marginalized DAGs

摘要： 我们提出了一种图形方法，用于推导有向无环图（DAG）模型中的不等式约束，其中一些变量是未被观测到的。 特别是我们证明了，如果任何两个观测变量在图中既不相邻，也不共享一个潜在父节点，那么离散模型的观测分布总是受到限制；这推广了众所周知的工具变量不等式。 该方法还提供了对干预分布的不等式，可用于界定因果效应。 所有这些约束都通过一种新的图形分离准则来描述，提供了一种简单直观的方法来推导它们。 显示英文摘要

摘要： We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of a discrete model is always restricted if any two observed variables are neither adjacent in the graph, nor share a latent parent; this generalizes the well known instrumental inequality. The method also provides inequalities on interventional distributions, which can be used to bound causal effects. All these constraints are characterized in terms of a new graphical separation criterion, providing an easy and intuitive method for their derivation.