Class of distance functions defined between probability distributions
In probability theory, integral probability metrics are types of distance functions between probability distributions, defined by how well a class of functions can distinguish the two distributions. Many important statistical distances are integral probability metrics, including the Wasserstein-1 distance and the total variation distance. In addition to theoretical importance, integral probability metrics are widely used in areas of statistics and machine learning.
The name "integral probability metric" was given by German statistician Alfred Müller;[1] the distances had also previously been called "metrics with a ζ-structure."[2]
^Müller, Alfred (June 1997). "Integral Probability Metrics and Their Generating Classes of Functions". Advances in Applied Probability. 29 (2): 429–443. doi:10.2307/1428011. JSTOR 1428011. S2CID 124648603.
^Zolotarev, V. M. (January 1984). "Probability Metrics". Theory of Probability & Its Applications. 28 (2): 278–302. doi:10.1137/1128025.
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