Wasserstein Distance Metric
A Wasserstein Distance Metric is a metric function that ...
- AKA: Kantorovich-Rubinstein Metric.
- See: Wasserstein, Probability Measure, Metric Space, Earth Mover's Distance, Wasserstein Auto-Encoder.
References
2018
- (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Wasserstein_metric Retrieved:2018-4-30.
- In mathematics, the Wasserstein or Kantorovich-Rubinstein metric or distance is a distance function defined between probability distributions on a given metric space [math]\displaystyle{ M }[/math] .
Intuitively, if each distribution is viewed as a unit amount of "dirt" piled on [math]\displaystyle{ M }[/math] , the metric is the minimum "cost" of turning one pile into the other, which is assumed to be the amount of dirt that needs to be moved times the distance it has to be moved. Because of this analogy, the metric is known in computer science as the earth mover's distance.
The name "Wasserstein distance" was coined by R. L. Dobrushin in 1970, after the Russian mathematician Leonid Vaseršteĭn who introduced the concept in 1969. Most English-language publications use the German spelling "Wasserstein" (attributed to the name "Vaserstein" being of German origin).
- In mathematics, the Wasserstein or Kantorovich-Rubinstein metric or distance is a distance function defined between probability distributions on a given metric space [math]\displaystyle{ M }[/math] .
2018
- (Tolstikhin et al., 2017) ⇒ Ilya Tolstikhin, Olivier Bousquet, Sylvain Gelly, and Bernhard Schoelkopf. (2017). “Wasserstein Auto-Encoders.” In: Proceedings of 6th International Conference on Learning Representations (ICLR-2018).