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

arXiv: https://arxiv.org/abs/2512.07074 · HTML: https://mlsanity.com/paper/2512.07074/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 72 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [OmniFold: A Method to Simultaneously Unfold All Observables](https://mlsanity.com/paper/1911.09107/) (2019)
- [How to GAN away Detector Effects](https://mlsanity.com/paper/1912.00477/) (2019)
- [End-To-End Latent Variational Diffusion Models for Inverse Problems in High Energy Physics](https://mlsanity.com/paper/2305.10399/) (2023)
- [Neural Networks for Full Phase-space Reweighting and Parameter Tuning](https://mlsanity.com/paper/1907.08209/) (2019)
- [An unfolding method based on conditional Invertible Neural Networks (cINN) using iterative training](https://mlsanity.com/paper/2212.08674/) (2022)
- [The Landscape of Unfolding with Machine Learning](https://mlsanity.com/paper/2404.18807/) (2024)
- [Improving Generative Model-based Unfolding with Schr"odinger Bridges](https://mlsanity.com/paper/2308.12351/) (2023)
- [Scaffolding Simulations with Deep Learning for High-dimensional Deconvolution](https://mlsanity.com/paper/2105.04448/) (2021)
- [Generative Unfolding with Distribution Mapping](https://mlsanity.com/paper/2411.02495/) (2024)
- [Unbinned Profiled Unfolding](https://mlsanity.com/paper/2302.05390/) (2023)
- [Simulation-Prior Independent Neural Unfolding Procedure](https://mlsanity.com/paper/2507.15084/) (2025)
- [A Particle Method for Solving Fredholm Equations of the First Kind](https://mlsanity.com/paper/2009.09974/) (2020)
- [Multidimensional Deconvolution with Profiling](https://mlsanity.com/paper/2409.10421/) (2024)

## Abstract (arXiv)

Statistically correcting measured cross sections for detector effects is an important step across many applications. In particle physics, this inverse problem is known as 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 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 OmniFold algorithm, we show how to extend machine learning-based unfolding to incorporate nuisance parameters. Our new algorithm, called Profile 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.