Causal Order Discovery based on Monotonic SCMs

TL;DR

This paper introduces a new sequential method for causal order discovery in monotonic SCMs that identifies root variables directly, avoiding complex optimization and sparsity assumptions, thus simplifying causal inference from observational data.

Contribution

The work presents a novel sequential procedure that directly detects causal order in monotonic SCMs without relying on sparsity or multiple independence tests.

Findings

Successfully identifies causal order by detecting root variables sequentially.

Outperforms Jacobian sparsity-based methods in accuracy and simplicity.

Eliminates the need for multiple independence tests to determine causal structure.

Abstract

In this paper, we consider the problem of causal order discovery within the framework of monotonic Structural Causal Models (SCMs), which have gained attention for their potential to enable causal inference and causal discovery from observational data. While existing approaches either assume prior knowledge about the causal order or use complex optimization techniques to impose sparsity in the Jacobian of Triangular Monotonic Increasing maps, our work introduces a novel sequential procedure that directly identifies the causal order by iteratively detecting the root variable. This method eliminates the need for sparsity assumptions and the associated optimization challenges, enabling the identification of a unique SCM without the need for multiple independence tests to break the Markov equivalence class. We demonstrate the effectiveness of our approach in sequentially finding the root variable, comparing it to methods that maximize Jacobian sparsity.