Graph Distance Based on Cause-Effect Estimands with Latents

TL;DR

This paper introduces a novel graph distance measure for ADMGs that assesses how graph differences impact cause-effect estimands, aiding evaluation of causal discovery methods especially with latent confounding.

Contribution

It proposes a new distance metric based on cause-effect estimands for ADMGs, addressing evaluation challenges in causal discovery with latent confounders.

Findings

The measure quantifies how graph perturbations affect cause-effect estimands.

Comparison shows the measure's effectiveness against existing metrics.

Analysis reveals the measure's behavior under various graph modifications.

Abstract

Causal discovery aims to recover graphs that represent causal relations among given variables from observations, and new methods are constantly being proposed. Increasingly, the community raises questions about how much progress is made, because properly evaluating discovered graphs remains notoriously difficult, particularly under latent confounding. We propose a graph distance measure for acyclic directed mixed graphs (ADMGs) based on the downstream task of cause-effect estimation under unobserved confounding. Our approach uses identification via fixing and a symbolic verifier to quantify how graph differences distort cause-effect estimands for different treatment-outcome pairs. We analyze the behavior of the measure under different graph perturbations and compare it against existing distance metrics.