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

Area of Science:

• Experimental Physics
• Machine Learning
• High Energy Physics

Background:

• Calibration is crucial in experimental physics for inferring unobservable quantities from measurements.
• Quantifying correlations between measured and unobservable quantities is essential.

Purpose of the Study:

• To develop a machine learning framework for frequentist maximum likelihood inference and uncertainty estimation.
• To quantify mutual information between unobservable and measured quantities.
• To simultaneously extract maximum likelihood values, uncertainties, and mutual information.

Main Methods:

• Utilized the Donsker-Varadhan representation of Kullback-Leibler divergence.
• Employed a novel Gaussian ansatz for parameterization.
• Integrated simultaneous extraction of key parameters within a single training process.

Main Results:

• Successfully extracted jet energy corrections and resolution factors from simulated CMS detector data.
• Achieved an improvement of over 15% in jet resolution compared to nominal CMS values.
• Demonstrated the framework's efficacy in high-dimensional feature spaces.

Conclusions:

• The proposed machine learning framework offers a unified approach to calibration and information quantification.
• This method enhances precision in experimental physics measurements, particularly in complex datasets like those from particle colliders.