Wasserstein distance — intuition.

hard

Answer

$'Earth mover's distance': minimum cost of transporting mass from P to Q where cost = distance \times mass.$
$W_{1}(P, \;Q)\; = \;\operatorname{inf}$
$Metrically meaningful even for disjoint distributions (unlike KL, which is infinite).$
$Uses: WGAN training stability, drift detection, optimal transport for domain adaptation, distribution comparison in imaging.$

Check yourself — multiple choice

Same as KL
'Earth mover' distance: min-cost transport of mass P → Q; metric even for disjoint distributions (KL fails); WGAN, drift, optimal transport
Random
Not real

Wasserstein: earth mover; metric on disjoint supports; WGAN / OT / drift.

#anomaly-detection#theory

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