# Gaussian Ansatz (v0.0.1)
[](https://github.com/rikab/GaussianAnsatz)
<!-- [](https://doi.org/10.5281/zenodo.7689890) -->
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)](https://arxiv.org/abs/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.
## Installation
### From PyPI
In your Python environment run
```
python -m pip install GaussianAnsatz
```
### From this repository locally
In your Python environment from the top level of this repository run
```
python -m pip install .
```
### From GitHub
In your Python environment run
```
python -m pip install "GaussianAnsatz @ git+https://github.com/rikab/GaussianAnsatz.git"
```
## Example Usage
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)](https://arxiv.org/abs/2205.03413)
## Dependencies
To use the `Gaussian Ansatz`, the following packages must be installed as prerequisites:
- [Tensorflow](https://github.com/tensorflow/tensorflow): A standard tensor operation library.
- [Energyflow](https://energyflow.network/): A suite of particle physics tools, including Energy Flow Networks and Particle FLow Networks
- Standard python packages: [numpy](https://numpy.org/), [scipy](https://scipy.org/), [matplotlib](https://matplotlib.org/)
## Citation
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"
}
## Changelog
- 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)](https://arxiv.org/abs/2205.03413)
Bugs, Fixes, Ideas, or Questions? Contact me at rikab@mit.edu
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