# On Suspicious Coincidences and Pointwise Mutual Information

arXiv: https://arxiv.org/abs/2203.08089 · HTML: https://mlsanity.com/paper/2203.08089/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 26 references that are in the map.
- First posted on arXiv 15 Mar 2022.

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

- [A Sobering Look at Tabular Data Generation via Probabilistic Circuits](https://mlsanity.com/paper/2603.23016/) (2026)
- [A Computational Model of Learning and Memory Using Structurally Dynamic Cellular Automata](https://mlsanity.com/paper/2501.06192/) (2024)

## Abstract (arXiv)

Barlow (1985) hypothesized that the co-occurrence of two events A and B is "suspicious" if P(A,B) gg P(A) P(B). We first review classical measures of association for 2 × 2 contingency tables, including Yule's Y (Yule, 1912), which depends only on the odds ratio λ, and is independent of the marginal probabilities of the table. We then discuss the mutual information (MI) and pointwise mutual information (PMI), which depend on the ratio P(A,B)/P(A)P(B), as measures of association. We show that, once the effect of the marginals is removed, MI and PMI behave similarly to Y as functions of λ. The pointwise mutual information is used extensively in some research communities for flagging suspicious coincidences, but it is important to bear in mind the sensitivity of the PMI to the marginals, with increased scores for sparser events.