Learning and scoring Gaussian latent variable causal models with unknown additive interventions

TL;DR

This paper introduces a maximum-likelihood approach for learning and scoring Gaussian latent variable causal models under unknown additive interventions, leveraging invariances to identify causal structures from perturbation data.

Contribution

It proposes a novel estimator that handles latent variables and unknown interventions, providing a graphical characterization of causal equivalence classes.

Findings

Successfully applied to synthetic data

Effective on real data from reservoirs and proteins

Outputs an equivalence class of causal structures

Abstract

With observational data alone, causal structure learning is a challenging problem. The task becomes easier when having access to data collected from perturbations of the underlying system, even when the nature of these is unknown. Existing methods either do not allow for the presence of latent variables or assume that these remain unperturbed. However, these assumptions are hard to justify if the nature of the perturbations is unknown. We provide results that enable scoring causal structures in the setting with additive, but unknown interventions. Specifically, we propose a maximum-likelihood estimator in a structural equation model that exploits system-wide invariances to output an equivalence class of causal structures from perturbation data. Furthermore, under certain structural assumptions on the population model, we provide a simple graphical characterization of all the DAGs in the interventional equivalence class. We illustrate the utility of our framework on synthetic data as well as real data involving California reservoirs and protein expressions. The software implementation is available as the Python package \emph{utlvce}.