Toward Universal Laws of Outlier Propagation
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915372899237888 |
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| author | Ebtekar, Aram Wang, Yuhao Janzing, Dominik |
| author_facet | Ebtekar, Aram Wang, Yuhao Janzing, Dominik |
| contents | 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 algorithmic Markov condition on a causal Bayesian network, we show that the randomness deficiency of a joint sample 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toward Universal Laws of Outlier Propagation Ebtekar, Aram Wang, Yuhao Janzing, Dominik Machine Learning 62D20 (Primary) 68Q30 (Secondary) G.3; E.4 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 algorithmic Markov condition on a causal Bayesian network, we show that the randomness deficiency of a joint sample 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. |
| title | Toward Universal Laws of Outlier Propagation |
| topic | Machine Learning 62D20 (Primary) 68Q30 (Secondary) G.3; E.4 |
| url | https://arxiv.org/abs/2502.08593 |