Causal Discovery in Linear Structural Causal Models with Deterministic Relations

TL;DR

This paper extends causal discovery methods to linear SCMs with deterministic relations and latent confounders, providing identifiability conditions and an algorithm validated on synthetic and real data.

Contribution

It introduces the first identifiability results for causal discovery in models with both deterministic relations and latent confounders, along with an algorithm for structure recovery.

Findings

Derived necessary and sufficient conditions for unique causal structure identifiability.

Proposed an algorithm for causal structure recovery under the new conditions.

Validated theoretical results on synthetic and real datasets.

Abstract

Linear structural causal models (SCMs) -- in which each observed variable is generated by a subset of the other observed variables as well as a subset of the exogenous sources -- are pervasive in causal inference and casual discovery. However, for the task of causal discovery, existing work almost exclusively focus on the submodel where each observed variable is associated with a distinct source with non-zero variance. This results in the restriction that no observed variable can deterministically depend on other observed variables or latent confounders. In this paper, we extend the results on structure learning by focusing on a subclass of linear SCMs which do not have this property, i.e., models in which observed variables can be causally affected by any subset of the sources, and are allowed to be a deterministic function of other observed variables or latent confounders. This allows for a more realistic modeling of influence or information propagation in systems. We focus on the task of causal discovery form observational data generated from a member of this subclass. We derive a set of necessary and sufficient conditions for unique identifiability of the causal structure. To the best of our knowledge, this is the first work that gives identifiability results for causal discovery under both latent confounding and deterministic relationships. Further, we propose an algorithm for recovering the underlying causal structure when the aforementioned conditions are satisfied. We validate our theoretical results both on synthetic and real datasets.