Score matching through the roof: linear, nonlinear, and latent variables causal discovery

Francesco Montagna, Philipp Michael Faller, Patrick Blöbaum, Elke Kirschbaum, Francesco Locatello
Proceedings of the Fourth Conference on Causal Learning and Reasoning, PMLR 275:552-605, 2025.

Abstract

Causal discovery from observational data holds great promise, but existing methods rely on strong assumptions about the underlying causal structure, often requiring full observability of all relevant variables. We tackle these challenges by leveraging the score function $\nabla \log p(X)$ of observed variables for causal discovery and propose the following contributions. First, we generalize the existing results of identifiability with the score to additive noise models with minimal requirements on the causal mechanisms. Second, we establish conditions for inferring causal relations from the score even in the presence of hidden variables; this result is two-faced: we demonstrate the score’s potential as an alternative to conditional independence tests to infer the equivalence class of causal graphs with hidden variables, and we provide the necessary conditions for identifying direct causes in latent variable models. Building on these insights, we propose a flexible algorithm for causal discovery across linear, nonlinear, and latent variable models, which we empirically validate.

Cite this Paper

BibTeX
@InProceedings{pmlr-v275-montagna25a, title = {Score matching through the roof: linear, nonlinear, and latent variables causal discovery}, author = {Montagna, Francesco and Faller, Philipp Michael and Bl\"{o}baum, Patrick and Kirschbaum, Elke and Locatello, Francesco}, booktitle = {Proceedings of the Fourth Conference on Causal Learning and Reasoning}, pages = {552--605}, year = {2025}, editor = {Huang, Biwei and Drton, Mathias}, volume = {275}, series = {Proceedings of Machine Learning Research}, month = {07--09 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v275/main/assets/montagna25a/montagna25a.pdf}, url = {https://proceedings.mlr.press/v275/montagna25a.html}, abstract = {Causal discovery from observational data holds great promise, but existing methods rely on strong assumptions about the underlying causal structure, often requiring full observability of all relevant variables. We tackle these challenges by leveraging the score function $\nabla \log p(X)$ of observed variables for causal discovery and propose the following contributions. First, we generalize the existing results of identifiability with the score to additive noise models with minimal requirements on the causal mechanisms. Second, we establish conditions for inferring causal relations from the score even in the presence of hidden variables; this result is two-faced: we demonstrate the score’s potential as an alternative to conditional independence tests to infer the equivalence class of causal graphs with hidden variables, and we provide the necessary conditions for identifying direct causes in latent variable models. Building on these insights, we propose a flexible algorithm for causal discovery across linear, nonlinear, and latent variable models, which we empirically validate.} }
Endnote
%0 Conference Paper %T Score matching through the roof: linear, nonlinear, and latent variables causal discovery %A Francesco Montagna %A Philipp Michael Faller %A Patrick Blöbaum %A Elke Kirschbaum %A Francesco Locatello %B Proceedings of the Fourth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2025 %E Biwei Huang %E Mathias Drton %F pmlr-v275-montagna25a %I PMLR %P 552--605 %U https://proceedings.mlr.press/v275/montagna25a.html %V 275 %X Causal discovery from observational data holds great promise, but existing methods rely on strong assumptions about the underlying causal structure, often requiring full observability of all relevant variables. We tackle these challenges by leveraging the score function $\nabla \log p(X)$ of observed variables for causal discovery and propose the following contributions. First, we generalize the existing results of identifiability with the score to additive noise models with minimal requirements on the causal mechanisms. Second, we establish conditions for inferring causal relations from the score even in the presence of hidden variables; this result is two-faced: we demonstrate the score’s potential as an alternative to conditional independence tests to infer the equivalence class of causal graphs with hidden variables, and we provide the necessary conditions for identifying direct causes in latent variable models. Building on these insights, we propose a flexible algorithm for causal discovery across linear, nonlinear, and latent variable models, which we empirically validate.
APA
Montagna, F., Faller, P.M., Blöbaum, P., Kirschbaum, E. & Locatello, F.. (2025). Score matching through the roof: linear, nonlinear, and latent variables causal discovery. Proceedings of the Fourth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 275:552-605 Available from https://proceedings.mlr.press/v275/montagna25a.html.

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