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.

翻译：对测量截面进行统计校正以消除探测器效应是众多应用领域中的重要步骤。在粒子物理学中，这一逆问题被称为反演。对于复杂仪器，其引入的畸变通常只能通过探测器模拟间接获知。现代机器学习技术为基于模拟的高维数据反演提供了高效方法。其中，首个成功应用于实验数据的方法是OmniFold算法——一种基于分类器的期望最大化过程。然而在实际应用中，前向模型往往仅近似确定，其相应不确定性通过干扰参数进行编码。本文以经过充分研究的OmniFold算法为基础，展示了如何将机器学习反演方法扩展至包含干扰参数的情形。我们提出的新算法命名为Profile OmniFold，通过高斯算例及基于大型强子对撞机CMS实验模拟数据的粒子物理案例研究验证了其有效性。