# Discrete Probabilistic Inverse Optimal Transport

arXiv: https://arxiv.org/abs/2112.09754 · HTML: https://mlsanity.com/paper/2112.09754/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 17 Dec 2021.

## Builds on (most cited first, 12 of 12)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Inverse optimal transport](https://mlsanity.com/paper/1905.03950/) (2019)
- [Learning to Match via Inverse Optimal Transport](https://mlsanity.com/paper/1802.03644/) (2018)
- [A mathematical theory of cooperative communication](https://mlsanity.com/paper/1910.02822/) (2019)
- [Unsupervised Hyperalignment for Multilingual Word Embeddings](https://mlsanity.com/paper/1811.01124/) (2018)
- [Regularized Optimal Transport is Ground Cost Adversarial](https://mlsanity.com/paper/2002.03967/) (2020)
- [Estimating matching affinity matrix under low-rank constraints](https://mlsanity.com/paper/1612.09585/) (2016)
- [Generalizing the theory of cooperative inference](https://mlsanity.com/paper/1810.02423/) (2018)

## Built on by (most cited first, 7 of 7)

- [Revisiting Deep Audio-Text Retrieval Through the Lens of Transportation](https://mlsanity.com/paper/2405.10084/) (2024)
- [Double-Bounded Optimal Transport for Advanced Clustering and Classification](https://mlsanity.com/paper/2401.11418/) (2024)
- [S-MolSearch: 3D Semi-supervised Contrastive Learning for Bioactive Molecule Search](https://mlsanity.com/paper/2409.07462/) (2024)
- [Differentiable Cost-Parameterized Monge Map Estimators](https://mlsanity.com/paper/2406.08399/) (2024)
- [Scalable unsupervised alignment of general metric and non-metric structures](https://mlsanity.com/paper/2406.13507/) (2024)
- [Bridging Vision and Language Concepts through Optimal Transport Semantic Flow](https://mlsanity.com/paper/2606.26891/) (2026)
- [Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximization](https://mlsanity.com/paper/2410.02628/) (2024)

## Abstract (arXiv)

Optimal transport (OT) formalizes the problem of finding an optimal coupling between probability measures given a cost matrix. The inverse problem of inferring the cost given a coupling is Inverse Optimal Transport (IOT). IOT is less well understood than OT. We formalize and systematically analyze the properties of IOT using tools from the study of entropy-regularized OT. Theoretical contributions include characterization of the manifold of cross-ratio equivalent costs, the implications of model priors, and derivation of an MCMC sampler. Empirical contributions include visualizations of cross-ratio equivalent effect on basic examples and simulations validating theoretical results.