Robust causal structure learning with some hidden variables

TL;DR

This paper presents a robust method for learning causal structures in DAGs with hidden variables, using a two-stage approach that improves accuracy in high-dimensional settings.

Contribution

A novel two-stage method leveraging low rank plus sparse framework for causal structure learning with hidden variables, enhancing accuracy and consistency.

Findings

Performs favorably compared to existing methods in structure recovery.

Achieves consistency in high-dimensional regimes.

Improves causal effect estimation accuracy.

Abstract

We introduce a new method to estimate the Markov equivalence class of a directed acyclic graph (DAG) in the presence of hidden variables, in settings where the underlying DAG among the observed variables is sparse, and there are a few hidden variables that have a direct effect on many of the observed ones. Building on the so-called low rank plus sparse framework, we suggest a two-stage approach which first removes the effect of the hidden variables, and then estimates the Markov equivalence class of the underlying DAG under the assumption that there are no remaining hidden variables. This approach is consistent in certain high-dimensional regimes and performs favourably when compared to the state of the art, both in terms of graphical structure recovery and total causal effect estimation.