Discussion of: Brownian distance covariance

By Arthur Gretton, Kenji Fukumizu, Bharath K. Sriperumbudur. 2009

82 citations recorded by the source corpus.

Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]

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Citations in the corpus

Hypothesis testing using pairwise distances and associated kernels (2012, methodology): “Second, results from Gretton et al. (2009a); Zhang et al. (2011) may be applied to get consistent two-sample and independence tests for the energy distance, without using bootstrap, which perform much better than the upper bound proposed by Székely et al. (2007) as an alternative to the bootstrap.”
Kernel Bayes' Rule (2010, methodology): “be solved via operations on the kernel means. Applications of this approach include homogeneity testing [14, 15], where the empirical means on the RKHS are compared directly, and independence testing [16, 17], where the mean of the joint distribution on the feature space is compared with that of the”
Using distance covariance for improved variable selection with application to learning genetic risk models (2014, unknown): “‡In [5], the author obtained equality here, which is incorrect.”
Gradient-Based Kernel Dimension Reduction for Regression (2014, methodology): “Various meth-ods for nonparametric inference also have been recently developed in this discipline (Gretton et al., 2005b, 2008, 2009, Fukumizu et al., 2008).”
A consistent multivariate test of association based on ranks of distances (2012, background): “Bickel and Xu (2009) offer a test based on an approximation of Renyi correlation, sincether is no explicit formula to compute the Renyi correlation.”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, methodology): “In the discussion, Rémillard (2009) based on Székely and Rizzo (2009), the author proposed using distance covariance based on the vectors of component-wise ranks (for general d1, d2).”
The affinely invariant distance correlation (2012, result): “Noting the results of Kosorok [11], Section 4; [12], we raise the possibility that the specific details can be devised in a judicious, data-dependent way so that the power of the test for independence increases when the transition is made to the affinely invariant distance correlation.”
Measuring nonlinear dependence in time‐series, a distance correlation approach (2012, background): “It is worth mentioning that in a short note, Rémillard (2009) suggested using autodistance correlation to measure nonlinear dependence in time-series.”
The distance correlation t-test of independence in high dimension (2013, background): “The first high dimensional extension of distance covariance is Kosorok’s discussion [8] of Székely and Rizzo [17].”
Independent Component Analysis via Distance Covariance (2013, methodology): “As described in Section 2.3 (also see R´emillard 2009), for continuous random variables, this dependency can be removed by applying the PIT component-wise.”
A Modified CRITIC Method to Estimate the Objective Weights of Decision Criteria (2021, background): “For instance, two criteria with a zero Pearson correlation coefficient may not be completely independent [44].”
Distribution-Free Consistent Independence Tests via Center-Outward Ranks and Signs (2019, background): “Indeed, in contrast to Székely and Rizzo (2009), Rémillard (2009) claimed that the methods based on marginal ranks are effective and as powerful as original ones when the sample size is moderately large and this idea has been explored in depth in Lin (2017).”
Energy statistics: A class of statistics based on distances (2013, unknown): “See also the discussion of Genovese [14].”
On the uniqueness of distance covariance (2012, background): “Feuerverger (2009, 1993) discusses the weight function in this context, and earlier considered a related bivariate statistic for testing independence based on characteristic functions.”
Kernel Bayes' rule: Bayesian inference with positive definite kernels (2013, methodology): “…al., 2007; Harchaoui et al., 2008; Gretton et al., 2009a, 2012), where the empirical means on the RKHS are compared directly, and independence testing (Gretton et al., 2008, 2009b), where the mean of the joint distribution on the feature space is compared with that of the product of the marginals.”
Distance covariance in metric spaces (2011, background): “The map α is injective also for all separable L spaces (1 < p < ∞): see Linde (1986b) or Gorin and Koldobskĭı (1987).”