Rank-Based Causal Discovery for Post-Nonlinear Models

Grigor Keropyan, David Strieder, Mathias Drton

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations

Abstract

Learning causal relationships from empirical observations is a central task in scientific research. A common method is to employ structural causal models that postulate noisy functional relations among a set of interacting variables. To ensure unique identifiability of causal directions, researchers consider restricted subclasses of structural causal models. Post-nonlinear (PNL) causal models constitute one of the most flexible options for such restricted subclasses, containing in particular the popular additive noise models as a further subclass. However, learning PNL models is not well studied beyond the bivariate case. The existing methods learn non-linear functional relations by minimizing residual dependencies and subsequently test independence from residuals to determine causal orientations. However, these methods can be prone to overfitting and, thus, difficult to tune appropriately in practice. As an alternative, we propose a new approach for PNL causal discovery that uses rank-based methods to estimate the functional parameters. This new approach exploits natural invariances of PNL models and disentangles the estimation of the nonlinear functions from the independence tests used to find causal orientations. We prove consistency of our method and validate our results in numerical experiments.

Original languageEnglish
Pages (from-to)7849-7870
Number of pages22
JournalProceedings of Machine Learning Research
Volume206
StatePublished - 2023
Event26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023 - Valencia, Spain
Duration: 25 Apr 202327 Apr 2023

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