# Toward Universal Laws of Outlier Propagation

arXiv: https://arxiv.org/abs/2502.08593 · HTML: https://mlsanity.com/paper/2502.08593/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 58 references that are in the map.
- First posted on arXiv 12 Feb 2025.

## Builds on (most cited first, 11 of 11)

- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Causal structure based root cause analysis of outliers](https://mlsanity.com/paper/1912.02724/) (2019)
- [Causal Inference-Based Root Cause Analysis for Online Service Systems with Intervention Recognition](https://mlsanity.com/paper/2206.05871/) (2022)
- [Root Cause Analysis of Outliers with Missing Structural Knowledge](https://mlsanity.com/paper/2406.05014/) (2024)
- [Backtracking Counterfactuals](https://mlsanity.com/paper/2211.00472/) (2022)
- [Root cause discovery via permutations and Cholesky decomposition](https://mlsanity.com/paper/2410.12151/) (2024)
- [The Implications of the No-Free-Lunch Theorems for Meta-induction](https://mlsanity.com/paper/2103.11956/) (2021)
- [Non-algorithmic theory of randomness](https://mlsanity.com/paper/1910.00585/) (2019)

## Built on by (most cited first, 3 of 3)

- [Formalizing and falsifying causal pathways of rare events](https://mlsanity.com/paper/2605.31254/) (2026)
- [Falsifying Causal Graphs With Outlier Events](https://mlsanity.com/paper/2607.12145/) (2026)
- [Understanding Generalization Requires Universal Induction](https://mlsanity.com/paper/2609.34458/) (2026)

## Abstract (arXiv)

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.