# Flows, Scaling, and Entropy Revisited: a Unified Perspective via Optimizing Joint Distributions

arXiv: https://arxiv.org/abs/2210.16456 · HTML: https://mlsanity.com/paper/2210.16456/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2022.

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

- [Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods](https://mlsanity.com/paper/2301.13006/) (2023)

## Abstract (arXiv)

In this short expository note, we describe a unified algorithmic perspective on several classical problems which have traditionally been studied in different communities. This perspective views the main characters -- the problems of Optimal Transport, Minimum Mean Cycle, Matrix Scaling, and Matrix Balancing -- through the same lens of optimization problems over joint probability distributions P(x,y) with constrained marginals. While this is how Optimal Transport is typically introduced, this lens is markedly less conventional for the other three problems. This perspective leads to a simple and unified framework spanning problem formulation, algorithm development, and runtime analysis.