Error Analysis of Triangular Optimal Transport Maps for Filtering

TL;DR

This paper analyzes estimation errors in optimal transport-based filtering algorithms, extending previous Brenier map error analyses to conditional maps, and demonstrates the effectiveness of an extended algorithm through numerical benchmarks.

Contribution

It extends error analysis of Brenier maps to conditional maps in filtering, and evaluates an improved optimal transport filtering algorithm with numerical experiments.

Findings

Error bounds for conditional Brenier maps in filtering

Extended optimal transport filtering algorithm performance

Numerical benchmarks on high-dimensional, non-Gaussian data

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.