Unbinned and Profiled Unfolding

Unfolding is an important procedure in particle physics experiments which corrects for detector effects and provides differential cross section measurements that can be used for a number of downstream tasks, such as extracting fundamental physics parameters. Traditionally, unfolding is done by discretizing the target phase space into a finite number of bins and is limited in the number of unfolded variables. Recently, there have been a number of proposals to perform unbinned and high-dimensional unfolding with machine learning. However, none of these methods allow for simultaneously constraining (profiling) nuisance parameters and thus they conflict with the standard approach, where data are unfolded and profiled. We propose a new machine learning-based unfolding method that can process and profile unbinned data. We first demonstrate the method with simple Gaussian examples and then show the impact on a simulated Higgs boson cross section measurement.