The Shape of Data by Colleen M. Farrelly & Yaé Ulrich Gaba

Author:Colleen M. Farrelly & Yaé Ulrich Gaba [M. Farrelly, Colleen & M. Farrelly, Colleen]
Language: eng
Format: epub
ISBN: 9781718503090
Published: 2023-06-27T00:00:00+00:00

Wasserstein Distance

In loose terms, Wasserstein distance compares the piles of probability weights stacked in two distributions. It’s often dubbed “earth-mover distance,” as the Wasserstein distance measures the cost and effort needed to move probability piles of one distribution to turn it into the comparison distribution. For more mathematically sophisticated readers, the pth Wasserstein distance can be calculated by taking the expected value of the joint distribution marginals to the pth power, finding the infimum over all join probability distributions of those random variables, and taking the pth root of the result. However, the details of this are beyond what is expected of readers, and we’ll stick with the intuition of earth-mover distance as we explore this metric. Let’s visualize two distributions of dirt piles to build some intuition behind this metric (Figure 5-9).

Figure 5-9: Two distributions of dirt piles akin to the type of probability density functions that could be compared using Wasserstein distance metrics

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