Learning Uncertainties the Frequentist Way: Calibration and Correlation in High Energy Physics

TL;DR

This paper introduces a machine learning framework for frequentist calibration in high energy physics that estimates uncertainties and correlations, demonstrated by improving jet resolution in CMS detector simulations.

Contribution

A novel Gaussian Ansatz-based approach for simultaneous maximum likelihood inference, uncertainty estimation, and mutual information quantification in high-dimensional physics data.

Findings

Improved jet resolution by over 15% in CMS simulations.

Unified framework for calibration, uncertainty, and correlation estimation.

Effective use of high-dimensional jet features for enhanced accuracy.

Abstract

Calibration is a common experimental physics problem, whose goal is to infer the value and uncertainty of an unobservable quantity Z given a measured quantity X. Additionally, one would like to quantify the extent to which X and Z are correlated. In this paper, we present a machine learning framework for performing frequentist maximum likelihood inference with Gaussian uncertainty estimation, which also quantifies the mutual information between the unobservable and measured quantities. This framework uses the Donsker-Varadhan representation of the Kullback-Leibler divergence -- parametrized with a novel Gaussian Ansatz -- to enable a simultaneous extraction of the maximum likelihood values, uncertainties, and mutual information in a single training. We demonstrate our framework by extracting jet energy corrections and resolution factors from a simulation of the CMS detector at the Large Hadron Collider. By leveraging the high-dimensional feature space inside jets, we improve upon the nominal CMS jet resolution by upwards of 15%.