Wasserstein distance

Target entity: Wasserstein distance
Context triple: [Wasserstein GAN, basedOn, Wasserstein distance]

• A. Hellinger distance
  Hellinger distance is a statistical measure of dissimilarity between probability distributions, derived from the Euclidean distance between their square-root densities and widely used in probability theory and information geometry.
• B. Wasserstein GAN
  Wasserstein GAN is a variant of generative adversarial networks that improves training stability and sample quality by optimizing the Wasserstein (Earth Mover’s) distance between real and generated data distributions.
• C. Optimal Transport: Old and New
  "Optimal Transport: Old and New" is a comprehensive monograph by Cédric Villani that develops the theory of optimal transport and its applications across analysis, geometry, and probability.
• D. Kolmogorov distance
  Kolmogorov distance is a statistical metric that measures the maximum difference between two cumulative distribution functions, commonly used to quantify convergence in distribution and in goodness-of-fit tests.
• E. Bhattacharyya distance
  Bhattacharyya distance is a statistical measure of similarity between two probability distributions, often used in pattern recognition and classification to quantify their overlap.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Wasserstein distance
Target entity description: Wasserstein distance is a metric from optimal transport theory that measures the minimal “cost” of transforming one probability distribution into another, widely used to compare distributions in statistics and machine learning.

• A. Hellinger distance
  Hellinger distance is a statistical measure of dissimilarity between probability distributions, derived from the Euclidean distance between their square-root densities and widely used in probability theory and information geometry.
• B. Wasserstein GAN
  Wasserstein GAN is a variant of generative adversarial networks that improves training stability and sample quality by optimizing the Wasserstein (Earth Mover’s) distance between real and generated data distributions.
• C. Optimal Transport: Old and New
  "Optimal Transport: Old and New" is a comprehensive monograph by Cédric Villani that develops the theory of optimal transport and its applications across analysis, geometry, and probability.
• D. Kolmogorov distance
  Kolmogorov distance is a statistical metric that measures the maximum difference between two cumulative distribution functions, commonly used to quantify convergence in distribution and in goodness-of-fit tests.
• E. Bhattacharyya distance
  Bhattacharyya distance is a statistical measure of similarity between two probability distributions, often used in pattern recognition and classification to quantify their overlap.
• F. None of above. chosen