Causal Link Discovery with Unequal Edge Error Tolerance

TL;DR

This paper introduces Neyman-Pearson causal discovery, a framework that controls different types of edge errors asymmetrically with finite-sample guarantees, using information-theoretic limits and a new algorithm for Gaussian models.

Contribution

It presents a novel causal discovery framework with asymmetric error control and finite-sample guarantees, along with the epsilon-CUT algorithm for linear Gaussian models.

Findings

Fundamental performance limits characterized by Rènyi divergence.

Epsilon-CUT algorithm provides finite-sample false positive guarantees.

Competitive performance with existing methods on Gaussian models.

Abstract

This paper proposes a novel framework for causal discovery with asymmetric error control, called Neyman-Pearson causal discovery. Despite the importance of applications where different types of edge errors may have different importance, current state-of-the-art causal discovery algorithms do not differentiate between the types of edge errors, nor provide any finite-sample guarantees on the edge errors. Hence, this framework seeks to minimize one type of error while keeping the other below a user-specified tolerance level. Using techniques from information theory, fundamental performance limits are found, characterized by the R\'enyi divergence, for Neyman-Pearson causal discovery. Furthermore, a causal discovery algorithm is introduced for the case of linear additive Gaussian noise models, called epsilon-CUT, that provides finite-sample guarantees on the false positive rate, while staying competitive with state-of-the-art methods.