# When Optimal Transport Meets Information Geometry

arXiv: https://arxiv.org/abs/2206.14791 · HTML: https://mlsanity.com/paper/2206.14791/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2022.

## Built on by (most cited first, 10 of 10)

- [Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descent](https://mlsanity.com/paper/2305.14076/) (2023)
- [InfoOT: Information Maximizing Optimal Transport](https://mlsanity.com/paper/2210.03164/) (2022)
- [Distributional Counterfactual Explanations With Optimal Transport](https://mlsanity.com/paper/2401.13112/) (2024)
- [Information Geometry of Wasserstein Statistics on Shapes and Affine Deformations](https://mlsanity.com/paper/2307.12508/) (2023)
- [Adaptive Pruning for Increased Robustness and Reduced Computational Overhead in Gaussian Process Accelerated Saddle Point Searches](https://mlsanity.com/paper/2510.06030/) (2025)
- [Wasserstein-Cram'er-Rao Theory of Unbiased Estimation](https://mlsanity.com/paper/2511.07414/) (2025)
- [Information Geometry for the Working Information Theorist](https://mlsanity.com/paper/2310.03884/) (2023)
- [Information Geometry for Wasserstein KL Divergence of Gaussian Measures on ℝn](https://mlsanity.com/paper/2503.24022/) (2025)
- [Scaling Limits of the Wasserstein information matrix on Gaussian Mixture Models](https://mlsanity.com/paper/2309.12997/) (2023)
- [Families of costs with zero and nonnegative MTW tensor in optimal transport and the c-divergences](https://mlsanity.com/paper/2401.00953/) (2024)

## Abstract (arXiv)

Information geometry and optimal transport are two distinct geometric frameworks for modeling families of probability measures. During the recent years, there has been a surge of research endeavors that cut across these two areas and explore their links and interactions. This paper is intended to provide an (incomplete) survey of these works, including entropy-regularized transport, divergence functions arising from c-duality, density manifolds and transport information geometry, the para-K"ahler and K"ahler geometries underlying optimal transport and the regularity theory for its solutions. Some outstanding questions that would be of interest to audience of both these two disciplines are posed. Our piece also serves as an introduction to the Special Issue on Optimal Transport of the journal Information Geometry.