Unfolding with a Wasserstein Loss

2026-03-21

AI Summary

This work addresses deconvolution and denoising in experimental sciences, where the classical Richardson–Lucy algorithm suffers from numerical errors and support mismatch due to its reliance on Kullback–Leibler divergence and data binning. The authors propose a data unfolding framework based on Wasserstein loss, which, under a transport-map noise model, establishes for the first time necessary and sufficient conditions for the existence and uniqueness of the optimization solution—thereby eliminating dependence on binning. They develop a scalable generalized Sinkhorn algorithm that operates solely on empirical observational data. Evaluated on one- and two-dimensional jet mass unfolding tasks, the method significantly outperforms classical approaches, demonstrating superior accuracy and robustness, particularly in regimes where binning artifacts are severe.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Data unfolding -- the removal of noise or artifacts from measurements -- is a fundamental task across the experimental sciences. Of particular interest are applications in physics, where the dominant approach is Richardson-Lucy (RL) deconvolution. The classical RL approach aims to find denoised data that, once passed through the noise model, is as close as possible to the measured data in terms of Kullback-Leibler (KL) divergence. This requires that the support of the measured data overlaps with the output of the noise model, a hypothesis typically enforced by binning, which introduces numerical error. As a counterpoint, the present work studies an alternative formulation using a Wasserstein loss. We establish sharp conditions for existence and uniqueness of optimizers, answering open questions of Li, et al., regarding necessary conditions for existence and uniqueness in the case of transport map noise models. We then develop a provably convergent generalized Sinkhorn algorithm to compute approximate optimizers. Our algorithm requires only empirical observations of the noise model and measured data and scales with the size of the data, rather than the ambient dimension. Numerical experiments on one- and two-dimensional problems inspired by jet mass unfolding in particle physics demonstrate that the optimal transport approach offers robust, accurate performance compared to classical RL deconvolution, particularly when binning artifacts are significant.

Problem

• data unfolding
• Wasserstein loss
• Richardson-Lucy deconvolution
• noise removal
• binning artifacts

Innovation

• Wasserstein loss
• data unfolding
• generalized Sinkhorn algorithm
• optimal transport
• Richardson-Lucy deconvolution