Toward Universal Laws of Outlier Propagation

Aram Ebtekar, Yuhao Wang, Dominik Janzing
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:1167-1183, 2025.

Abstract

When a variety of anomalous features motivate flagging different samples as *outliers*, Algorithmic Information Theory (AIT) offers a principled way to unify them in terms of a sample’s *randomness deficiency*. Subject to the Independence of Mechanisms Principle, we show that for a joint sample on the nodes of a causal Bayesian network, the randomness deficiency decomposes into a sum of randomness deficiencies at each causal mechanism. Consequently, anomalous observations can be attributed to their root causes, i.e., the mechanisms that behaved anomalously. As an extension of Levin’s law of randomness conservation, we show that weak outliers cannot cause strong ones. We show how these information theoretic laws clarify our understanding of outlier detection and attribution, in the context of more specialized outlier scores from prior literature.

Cite this Paper

BibTeX
@InProceedings{pmlr-v286-ebtekar25a, title = {Toward Universal Laws of Outlier Propagation}, author = {Ebtekar, Aram and Wang, Yuhao and Janzing, Dominik}, booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence}, pages = {1167--1183}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/ebtekar25a/ebtekar25a.pdf}, url = {https://proceedings.mlr.press/v286/ebtekar25a.html}, abstract = {When a variety of anomalous features motivate flagging different samples as *outliers*, Algorithmic Information Theory (AIT) offers a principled way to unify them in terms of a sample’s *randomness deficiency*. Subject to the Independence of Mechanisms Principle, we show that for a joint sample on the nodes of a causal Bayesian network, the randomness deficiency decomposes into a sum of randomness deficiencies at each causal mechanism. Consequently, anomalous observations can be attributed to their root causes, i.e., the mechanisms that behaved anomalously. As an extension of Levin’s law of randomness conservation, we show that weak outliers cannot cause strong ones. We show how these information theoretic laws clarify our understanding of outlier detection and attribution, in the context of more specialized outlier scores from prior literature.} }
Endnote
%0 Conference Paper %T Toward Universal Laws of Outlier Propagation %A Aram Ebtekar %A Yuhao Wang %A Dominik Janzing %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-ebtekar25a %I PMLR %P 1167--1183 %U https://proceedings.mlr.press/v286/ebtekar25a.html %V 286 %X When a variety of anomalous features motivate flagging different samples as *outliers*, Algorithmic Information Theory (AIT) offers a principled way to unify them in terms of a sample’s *randomness deficiency*. Subject to the Independence of Mechanisms Principle, we show that for a joint sample on the nodes of a causal Bayesian network, the randomness deficiency decomposes into a sum of randomness deficiencies at each causal mechanism. Consequently, anomalous observations can be attributed to their root causes, i.e., the mechanisms that behaved anomalously. As an extension of Levin’s law of randomness conservation, we show that weak outliers cannot cause strong ones. We show how these information theoretic laws clarify our understanding of outlier detection and attribution, in the context of more specialized outlier scores from prior literature.
APA
Ebtekar, A., Wang, Y. & Janzing, D.. (2025). Toward Universal Laws of Outlier Propagation. Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 286:1167-1183 Available from https://proceedings.mlr.press/v286/ebtekar25a.html.

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