Error Analysis of Triangular Optimal Transport Maps for Filtering
arXiv:2510.19283
The paper analyzes estimation errors of optimal‑transport‑based filtering algorithms, extending Brenier map error results to conditional Brenier maps and demonstrating the approach on non‑Gaussian, high‑dimensional problems.
Abstract
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.
82 pages, 7 figures