Abstract: Directed Causal Graphs (DAGs) capture causal relationships amongst a set of variables and they specify how interventional distributions relate to observational ones. Unobserved latent variables are represented in DAGs with edges having double arrows. Celebrated``do-calculus” introduced by Pearl relates invariances in interventional distributions to a specific causal graph with latents embodying expert knowledge. We consider the reverse problem of learning the equivalence class of causal graphs that could imply the observed invariances of the do-calculus. Given observational and interventional data obtained under soft interventions with known targets, we provide a complete characterization of the equivalence class of Causal DAGs. We also provide a sound learning algorithm to learn the equivalence class under additional faithfulness assumptions.
Karthikeyan Shanmugam is currently a Research Staff Member with the IBM Research AI group in NY. Previously, he was a Herman Goldstine Postdoctoral Fellow in the Math Sciences Division at IBM Research, NY. He obtained his Ph.D. in Electrical and Computer Engineering from UT Austin in 2016, MS degree in Electrical Engineering from USC in 2012, B.Tech and M.Tech degrees in Electrical Engineering from IIT Madras in 2010. His research interests broadly lie in Graph algorithms, Machine learning, Optimization, Coding Theory and Information Theory. In machine learning, his research focus is primarily on causal inference, online learning and explainable ML. He has also worked on problems relating to information flow, storage and caching over networks.