Wasserstein Distance

Wasserstein Distance measures how much "effort" it would take to transform one probability distribution into another. Imagine having two piles of sand shaped differently; the distance quantifies the minimal work needed to move the sand from the first shape to match the second, considering the amount and the distance each unit of sand must be moved. It provides a meaningful way to compare differences between distributions, especially when they have overlapping parts or are spread out, and is widely used in fields like machine learning and statistics to evaluate how similar or different two probability models are.