Learning Linear Gaussian Polytree Models with Interventions

The dominant approach in recent literature on causal discovery from interventional data is optimization of a model score. Although the scoring is straightforward in the sense that the optimization over DAGs refers to fully specified joint models for all observational and interventional data, the optimization landscape is very high-dimensional, making score-based algorithms infeasible for graphs with hundreds/thousands of nodes that are common in biological applications. This makes causal discovery difficult, in addition to many other challenges that remain such as departing from restrictive genericity assumptions on the underlying distributions and developing methodology for high-dimensional settings. In this article, to address these challenges, we depart from a score-based strategy and leverage special properties of polytrees to obtain a highly scalable "local" approach that learns from low-dimensional marginals. Our methods yield fast and consistent algorithms to learn linear Gaussian polytrees from interventional data.