TESTING FOR EQUAL DISTRIBUTIONS IN HIGH DIMENSION

By G'abor J. Sz'ekely, Maria L. Rizzo. 2004

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Citations in the corpus

DeepMDP: Learning Continuous Latent Space Models for Representation Learning (2019, methodology): “Energy distance: The energy distance E was first developed to compare distributions in high dimensions via a two sample test (Székely & Rizzo, 2004; Gretton et al., 2012).”
Demystifying MMD GANs (2018, background): “The energy distance (Székely & Rizzo, 2004; Lyons, 2013) is a measure of divergence between two probability measures, deﬁned as”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, neutral): “The energy distance between probability distributions P and Q as proposed in Székely and Rizzo (2004; 2005) is given by DE(P,Q) = 2EXY ‖X − Y ‖ − EXX′‖X −X ′‖ − EY Y ′‖Y − Y ′‖, (5.2) where X,X ′ ∼ P and Y, Y ′ ∼ Q.”
Interpretable Distribution Features with Maximum Testing Power (2016, methodology): “, 2012a) or energy distances (Székely and Rizzo, 2004; Baringhaus and Franz, 2004) have as their test statistic an integral probability metric, the Maximum Mean Discrepancy (Gretton et al.”
Hypothesis testing using pairwise distances and associated kernels (2012, methodology): “…a dramatic improvement for the sinusoidal perturbation, compared with the case q = 1 and the Gaussian kernel: values q = 1/3 (and smaller) yield virtually error-free performance even at high frequencies (note that q = 1 corresponds to the energy distance described in Székely & Rizzo (2004; 2005)).”
Deep Generative Markov State Models (2018, positive): “The standard ED, introduced in [28], is a metric between the distributions of random vectors, defined as DE (P(x),P(y)) = E [2 ‖x− y‖ − ‖x− x‖ − ‖y − y‖] (11)”
Computational Optimal Transport (2018, background): “The energy distance (or Cramer distance when d = 1) [Székely and Rizzo, 2004] associated to a distance d is defined as ‖α− β‖ED(X ,dp) def.”
B-tests: Low Variance Kernel Two-Sample Tests (2013, methodology): “Kernel test statistics include the maximum mean discrepancy [10, 6] (of which the energy distance is an example [18, 2, 22]), which is the distance between expected features of P and Q in the RKHS; the kernel Fisher discriminant [12], which is the distance between expected feature maps normalized by”
B-test: A Non-parametric, Low Variance Kernel Two-sample Test (2013, background): “These include the maximum mean discrepancy [9, 6] (of which the energy distance is an example [15, 2, 19]), which is the distance between expected features of P and Q in the RHKS; the kernel Fisher discriminant [11], which is the distance between expected feature maps normalized by the feature…”
Energy distance (2016, methodology): “Under an alternative hypothesis the statistic T tends to infinity stochastically as sample sizes tends to infinity, so the energy test for equal distributions that rejects the null for large values of T is consistent.(12) Because the null distribution of T depends on the distributions of X and Y, th”
Energy statistics: A class of statistics based on distances (2013, methodology): “(vi) Change point analysis based on Székely and Rizzo (2004) is applied in Kim et al. (2009) and Matteson and James (2012).”
Support points (2016, methodology): “structure of the energy distance in [67], one obtains for any distribution (locally) minimum energy sampling points which can outperform number-theoretic QMC methods.”
Principal Differences Analysis: Interpretable Characterization of Differences between Distributions (2015, background): “Unfortunately, this simplicity vanishes as the dimensionality d grows, and complex test-statistics have been designed to address some of the difficulties that appear in high-dimensional settings [5, 6, 7, 8].”
Decision Forests for Classification, Regression, Density Estimation, Manifold Learning and Semi-Supervised Learning (2011, methodology): “Alternatively one may consider the technique in [90].”