Efficient Concentration with Gaussian Approximation

Replication code for Efficient Concentration with Gaussian Approximation:

• efficient.py implements the efficient known-variance tail bounds and quantile bounds
• ebe.py implements the efficient empirical Berry-Esseen bound
• plot_quantile_bounds.ipynb reproduces the quantile bound, efficient quantile bound, and empirical quantile bound experiments
• monte_carlo_confidence.ipynb reproduces the Monte Carlo confidence intervals for numerical integration experiment

@article{
  austern2022efficient,
  title={Efficient Concentration with Gaussian Approximation},
  author={Morgane Austern and Lester Mackey},
  journal={arXiv preprint arXiv:2208.09922},
  year={2022}
}

Setup instructions

This code has been tested with Python 3.12.

conda create -n gauss python=3.12 --yes
conda activate gauss
pip install "numpy<2" scipy qmcpy matplotlib seaborn jupyterlab
pip install scikit-build cmake
pip install git+https://github.com/gostevehoward/confseq.git
pip install ttictoc sympy multiprocess