# Categorical Distributions of Maximum Entropy under Marginal Constraints

arXiv: https://arxiv.org/abs/2204.03406 · HTML: https://mlsanity.com/paper/2204.03406/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 42 references that are in the map.
- First posted on arXiv 7 Apr 2022.

## Builds on (most cited first, 3 of 3)

- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Inverse statistical problems: from the inverse Ising problem to data science](https://mlsanity.com/paper/1702.01522/) (2017)
- [Self-regularizing restricted Boltzmann machines](https://mlsanity.com/paper/1912.05634/) (2019)

## Built on by (most cited first, 1 of 1)

- [Entropy-based Characterization of Modeling Constraints](https://mlsanity.com/paper/2206.14105/) (2022)

## Abstract (arXiv)

The estimation of categorical distributions under marginal constraints summarizing some sample from a population in the most-generalizable way is key for many machine-learning and data-driven approaches. We provide a parameter-agnostic theoretical framework that enables this task ensuring (i) that a categorical distribution of Maximum Entropy under marginal constraints always exists and (ii) that it is unique. The procedure of iterative proportional fitting (IPF) naturally estimates that distribution from any consistent set of marginal constraints directly in the space of probabilities, thus deductively identifying a least-biased characterization of the population. The theoretical framework together with IPF leads to a holistic workflow that enables modeling any class of categorical distributions solely using the phenomenological information provided.