Confidence sets for Causal Discovery

Wednesday, September 25, 2024

Causal discovery aims to uncover the underlying causal relationships among variables in a multivariate dataset. Traditional methods primarily focus on estimating a single causal model or equivalence class, often neglecting the uncertainty inherent in the causal ordering process. In this talk, we present a novel framework for constructing confidence sets for causal orderings within the context of structural equation models (SEMs). Our approach leverages a residual bootstrap procedure to test the goodness-of-fit of causal orderings, providing a statistically rigorous method for quantifying uncertainty in causal discovery. We establish the asymptotic validity of the proposed confidence sets, which can be used to infer sub/supersets of ancestral relationships and to construct confidence intervals for causal effects that incorporate model uncertainty. This framework is particularly valuable when the signal strength is weak or when key modeling assumptions might be violated, offering a robust tool for analysts to avoid overconfidence in specific causal models. The methodology is computationally efficient, suitable for medium-sized problems, and maintains theoretical guarantees even as the number of variables increases. We illustrate the practical implications of our approach through an analysis of daily stock returns for industry portfolios, highlighting how different causal orderings can lead to significantly different conclusions, and how our confidence sets can inform more reliable causal inferences. This work represents a significant advancement in causal discovery, offering a new dimension of uncertainty quantification that enhances the robustness and reliability of causal inference in complex systems.

 

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Speaker/s

Mladen Kolar is a professor in the Department of Data Sciences and Operations at the USC Marshall School of Business. Mladen earned his PhD in Machine Learning from Carnegie Mellon University in 2013. His research focuses on high-dimensional statistical methods, probabilistic graphical models, and scalable optimization methods, driven by the need to uncover interesting and scientifically meaningful structures from observational data. Mladen was selected as a recipient of the 2024 Junior Leo Breiman Award for his outstanding contributions to these areas. He currently serves as an associate editor for the Journal of Machine Learning Research, the Annals of Statistics, the Journal of Computational and Graphical Statistics, and the New England Journal of Statistics in Data Science.

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