Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding

TL;DR

This paper introduces a novel score-based causal discovery method that leverages the statistical footprint of unobserved confounding, enabling the approximate recovery of sparse DAGs even with dense unobserved confounders.

Contribution

It proposes an adjusted scoring algorithm that exploits mechanisms beyond conditional independencies to identify causal structures under dense unobserved confounding.

Findings

Method recovers sparse DAGs approximately

Algorithm scales to high-dimensional data

Robust performance despite model assumption deviations

Abstract

Unobserved confounding is one of the greatest challenges for causal discovery. The case in which unobserved variables have a widespread effect on many of the observed ones is particularly difficult because most pairs of variables are conditionally dependent given any other subset, rendering the causal effect unidentifiable. In this paper we show that beyond conditional independencies, under the principle of independent mechanisms, unobserved confounding in this setting leaves a statistical footprint in the observed data distribution that allows for disentangling spurious and causal effects. Using this insight, we demonstrate that a sparse linear Gaussian directed acyclic graph among observed variables may be recovered approximately and propose an adjusted score-based causal discovery algorithm that may be implemented with general purpose solvers and scales to high-dimensional problems. We find, in addition, that despite the conditions we pose to guarantee causal recovery, performance in practice is robust to large deviations in model assumptions.