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Today we will discuss distances and metrics between distributions that are useful in statistics First, the evolutionary distance is. We will discuss them in two contexts

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There are metrics that are analytically useful in a variety of. Distance methods proceed in two steps We show that these common notions of metrics and divergences give rise to natural distances between borel probability measures defined on spaces of different dimensions, e.g., one on rm.

The optimal value of (5), denoted wd(μ, ν), is the wasserstein distance between μ and ν

An optimal solution z∗ to problem (5) is an optimal discriminator for the two probability distributions μ and ν. The wasserstein distance | which arises from the idea of optimal transport | is being used more and more in statistics and machine learning In these notes we review some of the basics about this.