Learning Linear Gaussian Polytree Models with Interventions
D. Tramontano L. Waldmann M. Drton E. Duarte
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.