Dual Likelihood for Causal Inference under Structure Uncertainty

David Strieder, Mathias Drton

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalProceedings of Machine Learning Research
Volume236
StatePublished - 2024
Event3rd Conference on Causal Learning and Reasoning, CLeaR 2024 - Los Angeles, United States
Duration: 1 Apr 20243 Apr 2024

Keywords

  • causal effects
  • dual likelihood
  • graphical models
  • linear structural causal models
  • uncertainty quantification

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