The Gaussian Ansatz is a machine learning framework for performing frequentist inference, complete with local uncertainty estimation, as described in "Learning Uncertainties the Frequentist Way: Calibration and Correlation in High Energy Physics" (arxiv:2205.03413). These models can be used to quickly estimate local resolutions of an inference $z$ given a measurement $x$, even if $x$ is very high-dimensional.

In your Python environment run

python -m pip install GaussianAnsatz

In your Python environment from the top level of this repository run

python -m pip install .

In your Python environment run

python -m pip install "GaussianAnsatz @ git+https://github.com/rikab/GaussianAnsatz.git"

For an example of how to use the Gaussian Ansatz, see the notebook examples/minimal_working_example.ipynb. This notebook contains example code for loading data, using pre-built DNN Gaussian Ansatz, pre-training and training, and extracting inferences with uncertainty estimates.

Additional, more complicated examples can be found in the JEC subfolder. The files here correspond exactly to the jet energy studies, as described in "Learning Uncertainties the Frequentist Way: Calibration and Correlation in High Energy Physics" (arxiv:2205.03413)

To use the Gaussian Ansatz, the following packages must be installed as prerequisites:

• Tensorflow: A standard tensor operation library.
• Energyflow: A suite of particle physics tools, including Energy Flow Networks and Particle FLow Networks
• Standard python packages: numpy, scipy, matplotlib

If you use the Gaussian Ansatz, please cite both the corresponding paper, "Learning Uncertainties the Frequentist Way: Calibration and Correlation in High Energy Physics"?:

@article{Gambhir:2022gua,
author = "Gambhir, Rikab and Nachman, Benjamin and Thaler, Jesse",
title = "{Learning Uncertainties the Frequentist Way: Calibration and Correlation in High Energy Physics}",
eprint = "2205.03413",
archivePrefix = "arXiv",
primaryClass = "hep-ph",
reportNumber = "MIT-CTP 5431",
doi = "10.1103/PhysRevLett.129.082001",
journal = "Phys. Rev. Lett.",
volume = "129",
number = "8",
pages = "082001",
year = "2022"

}

• v0.0.1: 17 April 2023. Now pip-installable!
• v0.0.0: 6 May 2022. Public release.

Based on the work in "Learning Uncertainties the Frequentist Way: Calibration and Correlation in High Energy Physics" (arxiv:2205.03413)

Bugs, Fixes, Ideas, or Questions? Contact me at rikab@mit.edu