# Proportional Analogies on Probability Distributions via Bayesian Updating

arXiv: https://arxiv.org/abs/2608.11724 · HTML: https://mlsanity.com/paper/2608.11724/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 25 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Abstraction and Analogy-Making in Artificial Intelligence](https://mlsanity.com/paper/2102.10717/) (2021)
- [An elementary introduction to information geometry](https://mlsanity.com/paper/1808.08271/) (2018)
- [Analogical Dissimilarity: Definition, Algorithms and Two Experiments in Machine Learning](https://mlsanity.com/paper/1401.3427/) (2014)
- [Measuring the Feasibility of Analogical Transfer using Complexity](https://mlsanity.com/paper/2206.11753/) (2022)
- [Any four real numbers are on all fours with analogy](https://mlsanity.com/paper/2407.18770/) (2024)

## Abstract (arXiv)

Analogies are quaternary relations of the form "A is to B as C is to D". Among the various formalizations of analogical reasoning, proportional analogies provide an important axiomatic framework by characterizing valid analogies through a set of postulates. While proportional analogies have been extensively studied over Boolean, symbolic, and real-valued domains, their extension to probability distributions remains largely unexplored. In this paper, we introduce a notion of proportional analogy for probability distributions based on Bayesian updating. Our approach builds upon the idea that two distributions are related whenever one can be transformed into the other through Bayesian updating induced by a suitable set of observations. We investigate this framework for several standard members of the exponential family and discuss how it naturally extends to arbitrary probability distributions through Gaussian mixture approximations.