Graphical methods for inequality constraints in marginalized DAGs

TL;DR

This paper introduces a graphical approach to derive inequality constraints in marginalized DAGs, enabling better understanding of causal relationships and bounds in models with unobserved variables.

Contribution

It generalizes the instrumental inequality and provides a new graphical separation criterion for deriving inequality constraints in DAG models with hidden variables.

Findings

Observed distributions are restricted under certain graph conditions.

The method derives inequalities on interventional distributions.

Provides an intuitive graphical separation criterion.

Abstract

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.