Information-Theoretic Causal Discovery in Topological Order

Sascha Xu, Sarah Mameche, Jilles Vreeken
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:2008-2016, 2025.

Abstract

Identifying causal relationships is a cornerstone task in science, but most data-driven methods offer ambiguous results or require restrictive assumptions. Recent work on the basis of information theory shows promising results across many domains, but leaves open how to provably identify causal graphs. Here, we develop a general information-theoretic framework called TOPIC for causal discovery in topological order. TOPIC is based on the universal measure of Kolmogorov complexity and is fully identifiable. We show that TOPIC’s guarantees extend to both the i.i.d. and non-i.i.d. continuous settings. Our evaluations on continuous, time series, and interventional data show that TOPIC, using domain-specific approximations of Kolmogorov complexity, learns faithful topological orderings and frequently outperforms specialized methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-xu25d, title = {Information-Theoretic Causal Discovery in Topological Order}, author = {Xu, Sascha and Mameche, Sarah and Vreeken, Jilles}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {2008--2016}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/xu25d/xu25d.pdf}, url = {https://proceedings.mlr.press/v258/xu25d.html}, abstract = {Identifying causal relationships is a cornerstone task in science, but most data-driven methods offer ambiguous results or require restrictive assumptions. Recent work on the basis of information theory shows promising results across many domains, but leaves open how to provably identify causal graphs. Here, we develop a general information-theoretic framework called TOPIC for causal discovery in topological order. TOPIC is based on the universal measure of Kolmogorov complexity and is fully identifiable. We show that TOPIC’s guarantees extend to both the i.i.d. and non-i.i.d. continuous settings. Our evaluations on continuous, time series, and interventional data show that TOPIC, using domain-specific approximations of Kolmogorov complexity, learns faithful topological orderings and frequently outperforms specialized methods.} }
Endnote
%0 Conference Paper %T Information-Theoretic Causal Discovery in Topological Order %A Sascha Xu %A Sarah Mameche %A Jilles Vreeken %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-xu25d %I PMLR %P 2008--2016 %U https://proceedings.mlr.press/v258/xu25d.html %V 258 %X Identifying causal relationships is a cornerstone task in science, but most data-driven methods offer ambiguous results or require restrictive assumptions. Recent work on the basis of information theory shows promising results across many domains, but leaves open how to provably identify causal graphs. Here, we develop a general information-theoretic framework called TOPIC for causal discovery in topological order. TOPIC is based on the universal measure of Kolmogorov complexity and is fully identifiable. We show that TOPIC’s guarantees extend to both the i.i.d. and non-i.i.d. continuous settings. Our evaluations on continuous, time series, and interventional data show that TOPIC, using domain-specific approximations of Kolmogorov complexity, learns faithful topological orderings and frequently outperforms specialized methods.
APA
Xu, S., Mameche, S. & Vreeken, J.. (2025). Information-Theoretic Causal Discovery in Topological Order. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:2008-2016 Available from https://proceedings.mlr.press/v258/xu25d.html.

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