# The most likely common cause

arXiv: https://arxiv.org/abs/2306.17557 · HTML: https://mlsanity.com/paper/2306.17557/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 52 references that are in the map.
- First posted on arXiv 30 Jun 2023.

## Builds on (most cited first, 4 of 4)

- [Causal versions of Maximum Entropy and Principle of Insufficient Reason](https://mlsanity.com/paper/2102.03906/) (2021)
- [Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables](https://mlsanity.com/paper/1506.03880/) (2015)
- [We Are Not Your Real Parents: Telling Causal from Confounded using MDL](https://mlsanity.com/paper/1901.06950/) (2019)
- [Observational nonidentifiability, generalized likelihood and free energy](https://mlsanity.com/paper/2002.07884/) (2020)

## Built on by (most cited first, 2 of 2)

- [Resolution of Simpson's paradox via the common cause principle](https://mlsanity.com/paper/2403.00957/) (2024)
- [Nonnegative matrix factorization and the principle of the common cause](https://mlsanity.com/paper/2509.03652/) (2025)

## Abstract (arXiv)

The common cause principle for two random variables A and B is examined in the case of causal insufficiency, when their common cause C is known to exist, but only the joint probability of A and B is observed. As a result, C cannot be uniquely identified (the latent confounder problem). We show that the generalized maximum likelihood method can be applied to this situation and allows identification of C that is consistent with the common cause principle. It closely relates to the maximum entropy principle. Investigation of the two binary symmetric variables reveals a non-analytic behavior of conditional probabilities reminiscent of a second-order phase transition. This occurs during the transition from correlation to anti-correlation in the observed probability distribution. The relation between the generalized likelihood approach and alternative methods, such as predictive likelihood and the minimum common cause entropy, is discussed. The consideration of the common cause for three observed variables (and one hidden cause) uncovers causal structures that defy representation through directed acyclic graphs with the Markov condition.