Wasserstein1

Wasserstein1 is a term that refers to the first Wasserstein distance, also known as the Earth Mover's distance. This metric quantifies the minimum "cost" to transform one probability distribution into another. Imagine two piles of dirt, each representing a probability distribution. The Wasserstein distance is the minimum amount of work needed to move the dirt from the first pile to match the shape of the second pile, where work is defined as the amount of dirt moved multiplied by the distance it is moved.

This distance is particularly useful in comparing probability distributions, especially when they are not overlapping or when dealing with high-dimensional data. Unlike other metrics that might struggle with such scenarios, the Wasserstein distance provides a meaningful measure of similarity. Its applications span various fields, including machine learning, computer vision, and natural language processing. In machine learning, it is often used to evaluate generative models, such as Generative Adversarial Networks (GANs), by measuring how well the generated data distribution matches the real data distribution. Its mathematical properties ensure a more stable and informative comparison in many complex settings.