# Scalable Approximate Algorithms for Optimal Transport Linear Models

arXiv: https://arxiv.org/abs/2504.04609 · HTML: https://mlsanity.com/paper/2504.04609/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 6 Apr 2025.

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

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport](https://mlsanity.com/paper/2006.00104/) (2020)
- [Parallelizing the dual revised simplex method](https://mlsanity.com/paper/1503.01889/) (2015)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [Clarabel: An interior-point solver for conic programs with quadratic objectives](https://mlsanity.com/paper/2405.12762/) (2024)
- [Unbalanced Optimal Transport through Non-negative Penalized Linear Regression](https://mlsanity.com/paper/2106.04145/) (2021)
- [An explicit analysis of the entropic penalty in linear programming](https://mlsanity.com/paper/1806.01879/) (2018)
- [Entropic Optimal Transport: Geometry and Large Deviations](https://mlsanity.com/paper/2102.04397/) (2021)
- [Beyond L1: Faster and Better Sparse Models with skglm](https://mlsanity.com/paper/2204.07826/) (2022)
- [Optimal spectral transportation with application to music transcription](https://mlsanity.com/paper/1609.09799/) (2016)

## Abstract (arXiv)

Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches often do not generalize readily to a broader class of linear models. In this work, we propose a novel algorithmic framework for solving a general class of non-negative linear regression models with an entropy-regularized OT datafit term, based on Sinkhorn-like scaling iterations. Our framework accommodates convex penalty functions on the weights (e.g. squared-ℓ2 and ℓ1 norms), and admits additional convex loss terms between the transported marginal and target distribution (e.g. squared error or total variation). We derive simple multiplicative updates for common penalty and datafit terms. This method is suitable for large-scale problems due to its simplicity of implementation and straightforward parallelization.