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

Armeen Taeb, Peter Bühlmann, Christina Heinze-Deml, Juan L. Gamella

Publication date: 18 January 2021

Abstract: With observational data alone, causal inference 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. Further, they assume perturbations on all observed variables. However, these assumptions are hard to justify if the nature of the perturbations is unknown. We provide results that enable scoring causal structures in this setting. 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.

Has companion code repository: https://github.com/juangamella/ut-lvce

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