Identifiability of Causal Graphs using Functional Models

TL;DR

This paper introduces Identifiable Functional Model Classes (IFMOCs) to uniquely determine causal graphs from data, extending beyond linear models and providing a practical algorithm with experimental validation.

Contribution

It proposes the first general identifiability result for causal graphs using IFMOCs, applicable to non-linear functional relationships, and offers a practical causal discovery algorithm.

Findings

Theoretical proof of causal graph identifiability under IFMOC assumptions.

Development of a practical algorithm for causal graph recovery.

Experimental validation on simulated data supports the theoretical results.

Abstract

This work addresses the following question: Under what assumptions on the data generating process can one infer the causal graph from the joint distribution? The approach taken by conditional independence-based causal discovery methods is based on two assumptions: the Markov condition and faithfulness. It has been shown that under these assumptions the causal graph can be identified up to Markov equivalence (some arrows remain undirected) using methods like the PC algorithm. In this work we propose an alternative by defining Identifiable Functional Model Classes (IFMOCs). As our main theorem we prove that if the data generating process belongs to an IFMOC, one can identify the complete causal graph. To the best of our knowledge this is the first identifiability result of this kind that is not limited to linear functional relationships. We discuss how the IFMOC assumption and the Markov and faithfulness assumptions relate to each other and explain why we believe that the IFMOC assumption can be tested more easily on given data. We further provide a practical algorithm that recovers the causal graph from finitely many data; experiments on simulated data support the theoretical findings.