# Randomized Transport Plans via Hierarchical Fully Probabilistic Design

arXiv: https://arxiv.org/abs/2408.02701 · HTML: https://mlsanity.com/paper/2408.02701/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 62 references that are in the map.
- First posted on arXiv 4 Aug 2024.

## Builds on (most cited first, 14 of 14)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [Scaling Algorithms for Unbalanced Transport Problems](https://mlsanity.com/paper/1607.05816/) (2016)
- [Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributions](https://mlsanity.com/paper/1905.02313/) (2019)
- [On Fairness, Diversity and Randomness in Algorithmic Decision Making](https://mlsanity.com/paper/1706.10208/) (2017)
- [Optimal Transport for Unsupervised Hallucination Detection in Neural Machine Translation](https://mlsanity.com/paper/2212.09631/) (2022)
- [Fair and Distributed Dynamic Optimal Transport for Resource Allocation over Networks](https://mlsanity.com/paper/2103.16618/) (2021)
- [Bayesian Inference for Optimal Transport with Stochastic Cost](https://mlsanity.com/paper/2010.09327/) (2020)
- [Fully Probabilistic Design for Optimal Transport](https://mlsanity.com/paper/2212.13912/) (2022)

## Abstract (arXiv)

An optimal randomized strategy for design of balanced, normalized mass transport plans is developed. It replaces -- but specializes to -- the deterministic, regularized optimal transport (OT) strategy, which yields only a certainty-equivalent plan. The incompletely specified -- and therefore uncertain -- transport plan is acknowledged to be a random process. Therefore, hierarchical fully probabilistic design (HFPD) is adopted, yielding an optimal hyperprior supported on the set of possible transport plans, and consistent with prior mean constraints on the marginals of the uncertain plan. This Bayesian resetting of the design problem for transport plans -- which we call HFPD-OT -- confers new opportunities. These include (i) a strategy for the generation of a random sample of joint transport plans; (ii) randomized marginal contracts for individual source-target pairs; and (iii) consistent measures of uncertainty in the plan and its contracts. An application in fair market matching is outlined, in which HFPD-OT enables the recruitment of a more diverse subset of contracts -- than is possible in classical OT -- into the delivery of an expected plan.