https://github.com/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.
https://github.com/fabriziomusacchio/wasserstein_distance_demo

optimal-transport python wasserstein-distance

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

• Host: GitHub
• URL: https://github.com/fabriziomusacchio/wasserstein_distance_demo
• Owner: FabrizioMusacchio
• Created: 2023-07-24T08:21:12.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2023-07-28T10:36:43.000Z (over 1 year ago)
• Last Synced: 2023-07-28T11:37:29.298Z (over 1 year ago)
• Topics: optimal-transport, python, wasserstein-distance
• Language: Python
• Homepage: https://www.fabriziomusacchio.com/blog/2023-07-22-wasserstein_distance
• Size: 22.8 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Wasserstein metric

This repository contains the code for the following blog posts:

* [Wasserstein distance and optimal transport](https://www.fabriziomusacchio.com/blog/2023-07-22-wasserstein_distance)

* [Wasserstein distance via entropy regularization (Sinkhorn algorithm)](https://www.fabriziomusacchio.com/blog/2023-07-23-wasserstein_distance_skinhorn)

* [Approximating the Wasserstein distance with cumulative distribution functions ](https://www.fabriziomusacchio.com/blog/2023-07-24-wasserstein_distance_cdf_approximation/)

* [Comparing Wasserstein distance, sliced Wasserstein distance, and L2 norm ](https://www.fabriziomusacchio.com/blog/2023-07-26-wasserstein_vs_l2_norm/)

* [Probability distance metrics in machine learning](https://www.fabriziomusacchio.com/blog/2023-07-28-probability_density_metrics/)

For further details, please refer to these posts.

For reproducibility:

```powershell

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):

![img](images/wasserstein_distributions.png)

The according distance (cost) matrix:

![img](images/wasserstein_cost_matrix.png)

And the resulting optimal transport plan:

![img](images/wasserstein_optimal_transport_linear_programming.png)

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

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

![img](images/wasserstein_l2_animation_m2.gif)

![img](images/wasserstein_l2_animation_s2.gif)

Comparing various probability distance metrics:

![img](images/distance_evolution_discrete_mean2.gif)

![img](images/distance_evolution_discrete_std2.gif)