Learning Linear Gaussian Polytree Models with Interventions

We present a consistent and highly scalable local approach to learn the causal structure of a linear Gaussian polytree using data from interventional experiments with known intervention targets. Our methods first learn the skeleton of the polytree and then orient its edges. The output is a CPDAG representing the interventional equivalence class of the polytree of the true underlying distribution. The skeleton and orientation recovery procedures we use rely on second order statistics and low-dimensional marginal distributions. We assess the performance of our methods under different scenarios in synthetic data sets and apply our algorithm to learn a polytree in a gene expression interventional data set. Our simulation studies demonstrate that our approach is fast, has good accuracy in terms of structural Hamming distance, and handles problems with thousands of nodes.
Comment: To be published in: IEEE Journal on Selected Areas in Information Theory, Special Issue: Causality: Fundamental Limits and Applications