Dual Likelihood for Causal Inference Under Structure Uncertainty

MCML Authors

David Strieder

→ Group Mathias Drton
 Mathematical Statistics

Mathias Drton

Prof. Dr.

Principal Investigator

Mathematical Statistics

Abstract

Knowledge of the underlying causal relations is essential for inferring the effect of interventions in complex systems. In a widely studied approach, structural causal models postulate noisy functional relations among interacting variables, where the underlying causal structure is then naturally represented by a directed graph whose edges indicate direct causal dependencies. In the typical application, this underlying causal structure must be learned from data, and thus, the remaining structure uncertainty needs to be incorporated into causal inference in order to draw reliable conclusions. In recent work, test inversions provide an ansatz to account for this data-driven model choice and, therefore, combine structure learning with causal inference. In this article, we propose the use of dual likelihood to greatly simplify the treatment of the involved testing problem. Indeed, dual likelihood leads to a closed-form solution for constructing confidence regions for total causal effects that rigorously capture both sources of uncertainty: causal structure and numerical size of nonzero effects. The proposed confidence regions can be computed with a bottom-up procedure starting from sink nodes. To render the causal structure identifiable, we develop our ideas in the context of linear causal relations with equal error variances.

inproceedings

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CLeaR 2024

3rd Conference on Causal Learning and Reasoning. Los Angeles, CA, USA, Apr 01-03, 2024.

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Authors

D. Strieder • M. Drton

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Links

URL

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Research Area

 A1 | Statistical Foundations & Explainability