Code for '' Projected Statistical Methods for Distributional Data on the Real Line with the Wasserstein Metric ''

Requirements

The code was developed and tested on an Ubuntu 18.04 machine with the following libraries

python 3.8
numpy==1.18.2
scipy==1.4.1
scikit-learn==0.22.2.post1
pyomo==5.7
qpsolvers==1.1

Moreover, the optimization library Ipopt (version 3.12.12) was used and called via pyomo. To install ipopt, follow the instructions at https://coin-or.github.io/Ipopt/INSTALL.html The Ipopt solver is used only to compute the global and nested geodesic PCA, not the projected one.

Directory structure

The actual implementation of the algorithms and some utilities is found in the folder pwass

The folder scripts contain python scripts to run the simulated examples. For instance, to run the Bernstein simulation, it is sufficient to run from the terminal (from the current / root folder):

python3 -m scripts.bernstein_simulation

Default arguments used in the simulations are given for all the command line arguments.

The folder data contains the Covid-19 deaths dataset and the Wind speed dataset.

Finally in the current folder some Jupyter Notebooks are present, to reproduce all the plots in the manuscript and to run some of the simulations