Confidence Sets for Causal Orderings
Abstract
Causal discovery procedures aim to deduce causal relationships among variables in a multivariate dataset. While various methods have been proposed for estimating a single causal model or a single equivalence class of models, less attention has been given to quantifying uncertainty in causal discovery in terms of confidence statements. The primary challenge in causal discovery is determining a causal ordering among the variables. Our research offers a framework for constructing confidence sets of causal orderings that the data do not rule out. Our methodology applies to structural equation models and is based on a residual bootstrap procedure to test the goodness-of-fit of causal orderings. We demonstrate the asymptotic validity of the confidence set constructed using this goodness-of-fit test and explain how the confidence set may be used to form sub/supersets of ancestral relationships as well as confidence intervals for causal effects that incorporate model uncertainty.
Type
Publication
Journal of the American Statistical Association, 121(553), 690–703
Authors
Professor of Data Sciences and Operations
Mladen Kolar is a Professor of Data Sciences and Operations at the University of Southern California Marshall School of Business and a Visiting Professor of Statistics and Data Science at Mohamed bin Zayed University of Artificial Intelligence. Before joining USC, he was on the faculty of the University of Chicago Booth School of Business. His research is focused on high-dimensional statistical methods, graphical models, varying-coefficient models and data mining, driven by the need to uncover interesting and scientifically meaningful structures from observational data. He is a Fellow of the Institute of Mathematical Statistics.