Wasserstein Distance
The Wasserstein Distance, also known as the Earth Mover's Distance, is a measure of the distance between two probability distributions. It quantifies how much "work" is needed to transform one distribution into another by considering the optimal way to move probability mass. This concept is particularly useful in fields like statistics, machine learning, and computer vision.
In practical terms, the Wasserstein Distance can be visualized as the minimum cost of transporting goods from one pile to another, where the cost is determined by the distance moved. This makes it a powerful tool for comparing distributions, especially when they have different shapes or support.