# Wasserstein Distance to Independence Models

arXiv: https://arxiv.org/abs/2003.06725 · HTML: https://mlsanity.com/paper/2003.06725/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2020.

## Built on by (most cited first, 4 of 4)

- [Geometry of Linear Convolutional Networks](https://mlsanity.com/paper/2108.01538/) (2021)
- [The Geometry of Memoryless Stochastic Policy Optimization in Infinite-Horizon POMDPs](https://mlsanity.com/paper/2110.07409/) (2021)
- [Discrete Optimal Transport with Independent Marginals is #P-Hard](https://mlsanity.com/paper/2203.01161/) (2022)
- [Temporal Robustness in Discrete Time Linear Dynamical Systems](https://mlsanity.com/paper/2505.02347/) (2025)

## Abstract (arXiv)

An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. Any metric on the set of joint states of the random variables induces a Wasserstein metric on the probability simplex. The unit ball of this polyhedral norm is dual to the Lipschitz polytope. Given any data distribution, we seek to minimize its Wasserstein distance to a fixed independence model. The solution to this optimization problem is a piecewise algebraic function of the data. We compute this function explicitly in small instances, we examine its combinatorial structure and algebraic degrees in the general case, and we present some experimental case studies.