The Wasserstein family

The Wasserstein family consists of mathematical tools used to measure the difference between two probability distributions or datasets. Think of it as the minimal “cost” to transform one distribution into another, where “cost” considers both the amount of change and the distance it occurs. This measure, known as the Wasserstein distance, captures more nuanced differences than simple statistics like mean or variance. It’s particularly useful in fields like machine learning and optimal transport, helping compare complex data distributions in a meaningful way that reflects their underlying structure.