Causal Discovery in Linear Structural Causal Models with Deterministic Relations
Abstract
Linear structural causal models (SCMs)- in which each observed variable is generated by a subset of the other observed variables as well as a subset of the exogenous sources- are pervasive in causal inference and casual discovery. However, for the task of causal discovery, existing work almost exclusively focus on the submodel where each observed variable is associated with a distinct source with non-zero variance. This results in the restriction that no observed variable can deterministically depend on other observed variables or latent confounders. In this paper, we extend the results on structure learning by focusing on a subclass of linear SCMs which do not have this property, i.e., models in which observed variables can be causally affected by any subset of the sources, and are allowed to be a deterministic function of other observed variables or latent confounders. This allows for a more realistic modeling of influence or information propagation in systems. We focus on the task of causal discovery form observational data generated from a member of this subclass. We derive a set of necessary and sufficient conditions for unique identifiability of the causal structure. To the best of our knowledge, this is the first work that gives identifiability results for causal discovery under both latent confounding and deterministic relationships. Further, we propose an algorithm for recovering the underlying causal structure when the aforementioned conditions are satisfied. We validate our theoretical results both on synthetic and real datasets.
Recommended Citation
Y. Yang et al., "Causal Discovery in Linear Structural Causal Models with Deterministic Relations," Proceedings of Machine Learning Research, vol. 177, pp. 944 - 993, Journal of Machine Learning Research (JMLR), Jan 2022.
Department(s)
Electrical and Computer Engineering
Keywords and Phrases
Blind Source Separation; Causal Discovery; Deterministic Relations; Structural Causal Models
International Standard Serial Number (ISSN)
2640-3498
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 The Authors, All rights reserved.
Publication Date
01 Jan 2022
Comments
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Grant 200021_204355 /1