# On a Relation Between the Rate-Distortion Function and Optimal Transport

arXiv: https://arxiv.org/abs/2307.00246 · HTML: https://mlsanity.com/paper/2307.00246/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 17 references that are in the map.
- First posted on arXiv 1 Jul 2023.

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

- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Sinkhorn Natural Gradient for Generative Models](https://mlsanity.com/paper/2011.04162/) (2020)
- [Neural Estimation of the Rate-Distortion Function With Applications to Operational Source Coding](https://mlsanity.com/paper/2204.01612/) (2022)

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

- [Estimating the Rate-Distortion Function by Wasserstein Gradient Descent](https://mlsanity.com/paper/2310.18908/) (2023)

## Abstract (arXiv)

We discuss a relationship between rate-distortion and optimal transport (OT) theory, even though they seem to be unrelated at first glance. In particular, we show that a function defined via an extremal entropic OT distance is equivalent to the rate-distortion function. We numerically verify this result as well as previous results that connect the Monge and Kantorovich problems to optimal scalar quantization. Thus, we unify solving scalar quantization and rate-distortion functions in an alternative fashion by using their respective optimal transport solvers.