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 Letter, 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 upward of 15%.

• Received 23 May 2022
• Accepted 25 July 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.082001

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Published by the American Physical Society