Estimating epistemic and aleatoric uncertainties for Omnifolded distributions

Development of machine learning techniques and modern hardware have made Neural Networks ubiquitous in experimental sciences. One particularly stark example of this would be the Omnifold method of deconvoluting detector effects from high energy physics measurements. In the various published and active measurements where Omnifold has been tried and tested, the uncertainties introduced by the method's usage of neural networks are usually calculated ``lump-sum" from the variations caused in the unfolded distributions by varying the initial seed for the random processes involved, like initialization of model weights, train-validation split, etc.



In this study, we explore the potential for a more granular treatment of uncertainties introduced by Omnifold, rather than only calculating the overall uncertainty. In the recent years, the problem of decomposing uncertainties propagated from the training data distributions ( Epistemic uncertainties, can be reduced by collecting more data) and uncertainties introduced by the stocastic nature of initializing and training neural networks ( Aleatoric uncertainties, intrinsic to the model used), has been gaining interest among data scientists, and a formalization of estimating epistemic and aleatoric uncertainties would give us a robust metric to asses the quality of unfolding done by the Omnifold models we use. For example, if the unfolded distributions show large variations based on initialization of model weights (high aleatoric uncertainity relative to the epistemic uncertainty), then a different model architecture might be advisable.



We have shown estimates of epistemic and aleatoric uncertainties for Omnifold methods used in the estimation of generalized jet angularity distributions from 200 GeV p+p collision data collected by the STAR experiment. Dependence of these uncertainties on uncertainties in experimental data is also shown.