Learning Uncertainties the Frequentist Way: Calibration and Correlation in High Energy Physics,Physical Review Letters

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Learning Uncertainties the Frequentist Way: Calibration and Correlation in High Energy Physics
Physical Review Letters ( IF 8.1 ) Pub Date : 2022-08-15 , DOI: 10.1103/physrevlett.129.082001
Rikab Gambhir _{1,

2} , Benjamin Nachman _{3,

4} , Jesse Thaler _{1,

2}

Affiliation

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%.

中文翻译：

以频率论的方式学习不确定性：高能物理中的校准和相关性

校准是一个常见的实验物理问题，其目标是推断不可观测量的值和不确定性

Z

给定一个测量量

X

. 此外，人们想量化

X

和

Z

是相关的。在这封信中，我们提出了一个机器学习框架，用于使用高斯不确定性估计执行频率最大似然推断，该框架还量化了不可观察量和测量量之间的互信息。该框架使用 Kullback-Leibler 散度的 Donsker-Varadhan 表示（使用新的 Gaussian ansatz 进行参数化），以便在一次训练中同时提取最大似然值、不确定性和互信息。我们通过从大型强子对撞机的 CMS 探测器模拟中提取射流能量校正和分辨率因子来展示我们的框架。通过利用射流内部的高维特征空间，我们将标称 CMS 射流分辨率提高了 15% 以上。

更新日期：2022-08-15

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