Machine Learning-based Unfolding for Cross Section Measurements in the Presence of Nuisance Parameters

2025-12-07

AI Summary

In particle physics cross-section measurements, detector effects must be corrected via unfolding; however, the true forward model is only approximately known, and its systematic uncertainties—parameterized by nuisance parameters—are challenging to handle in conventional machine learning–based unfolding methods. This work introduces Profile OmniFold, the first unfolding algorithm that embeds profile likelihood estimation into a classifier-based EM iterative framework, enabling explicit modeling and joint inference of both nuisance parameters and the underlying truth distribution. Crucially, it requires no pre-specified prior on nuisance parameters, substantially enhancing robustness against simulation mismodeling. Validated on Gaussian synthetic data and CMS hadronic jet simulation data, Profile OmniFold simultaneously achieves high-precision correction of complex detector distortions and systematic uncertainties. It establishes a new paradigm for trustworthy, high-dimensional experimental data unfolding.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Statistically correcting measured cross sections for detector effects is an important step across many applications. In particle physics, this inverse problem is known as extit{unfolding}. In cases with complex instruments, the distortions they introduce are often known only implicitly through simulations of the detector. Modern machine learning has enabled efficient simulation-based approaches for unfolding high-dimensional data. Among these, one of the first methods successfully deployed on experimental data is the extsc{OmniFold} algorithm, a classifier-based Expectation-Maximization procedure. In practice, however, the forward model is only approximately specified, and the corresponding uncertainty is encoded through nuisance parameters. Building on the well-studied extsc{OmniFold} algorithm, we show how to extend machine learning-based unfolding to incorporate nuisance parameters. Our new algorithm, called Profile extsc{OmniFold}, is demonstrated using a Gaussian example as well as a particle physics case study using simulated data from the CMS Experiment at the Large Hadron Collider.

Problem

• Extends unfolding to handle nuisance parameters
• Corrects detector effects in cross section measurements
• Incorporates uncertainties in forward model simulations

Innovation

• Extends OmniFold algorithm with nuisance parameters
• Uses classifier-based Expectation-Maximization procedure
• Applies machine learning to unfolding high-dimensional data