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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. In this talk, we will describe methods that use such perturbation data to identify plausible causal mechanisms and to obtain robust predictions. Specifically, in the context of Gaussian linear structural equation models, we first characterize the interventional equivalence class of DAGs. We then leverage these results to study high-dimensional consistency guarantees of a l0-penalized maximum likelihood estimator for learning said class. Since solving this estimator is generally intractable, we design a procedure which proceeds greedily in the space of interventional equivalent models and show that our procedure is competitive especially in low-sample size settings. Finally, we describe how to exploit heterogeneity in the perturbation data to produce distributionally robust estimators. 

This work was conducted in collaboration with Peter Buehlmann, Juan Gamella, Felix Hafenmair, Christina Heinze-Deml, and Xinwei Shen.