Learning Linear Gaussian Polytree Models With Interventions

• Published in: IEEE journal on selected areas in information theory 2023, Vol.4, p.569-578
• Main Authors: Tramontano, Daniele, Waldmann, L., Drton, M., Duarte, Eliana
• Format: Article
• Language: English
• Subjects: Algorithms; Causal discovery; Covariance matrices; Datasets; Gaussian processes; Gene expression; Graph theory; interventions; linear structural equation model; Markov processes; Mathematical models; Optimization; Polytrees; Synthetic data; Tree graphs
• ISSN: 2641-8770; 2641-8770
• DOI: 10.1109/JSAIT.2023.3328429

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.