FabrizioMusacchio / Wasserstein_distance_demo

This repository contains the code for some blog posts on the Wasserstein metric. For further details, please refer to the corresponding posts.

Wasserstein metric

This repository contains the code for the following blog posts:

• Wasserstein distance and optimal transport
• Wasserstein distance via entropy regularization (Sinkhorn algorithm)
• Approximating the Wasserstein distance with cumulative distribution functions
• Comparing Wasserstein distance, sliced Wasserstein distance, and L2 norm
• Probability distance metrics in machine learning

For further details, please refer to these posts.

For reproducibility:

conda create -n wasserstein -y python=3.9
conda activate wasserstein
conda install mamba -y
mamba install -y numpy matplotlib scikit-learn scipy pot ipykernel
pip install POT

Examples

Two example distributions (source and target):

The according distance (cost) matrix:

And the resulting optimal transport plan:

The corresponding Wasserstein distance is $W_1 = \sim0.1658$.

Comparing Wasserstein distance, sliced Wasserstein distance (SWD), and L2 norm:

Comparing various probability distance metrics: