# Error Analysis of Triangular Optimal Transport Maps for Filtering

arXiv: https://arxiv.org/abs/2510.19283 · HTML: https://mlsanity.com/paper/2510.19283/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2025.

## Built on by (most cited first, 3 of 3)

- [Error Analysis of Bayesian Inverse Problems with Generative Priors](https://mlsanity.com/paper/2601.17374/) (2026)
- [Conditional Sampling via Wasserstein Autoencoders and Triangular Transport](https://mlsanity.com/paper/2604.02644/) (2026)
- [Generative models for simulation based filtering: Formulations and Empirical Comparisons](https://mlsanity.com/paper/2609.16317/) (2026)

## Abstract (arXiv)

We present a systematic analysis of estimation errors for a class of optimal transport based algorithms for filtering and data assimilation. Along the way, we extend previous error analyses of Brenier maps to the case of conditional Brenier maps that arise in the context of simulation based inference. We then apply these results in a filtering scenario to analyze the optimal transport filtering algorithm of Al-Jarrah et al. (2024, ICML). An extension of that algorithm along with numerical benchmarks on various non-Gaussian and high-dimensional examples are provided to demonstrate its effectiveness and practical potential.