Consistent Nonparametric Tests of Independence

By Arthur Gretton, László Györfi. 2010

135 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Statistics and Probability

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Citations in the corpus

A Kernel Test of Goodness of Fit (2016, background): “Such space partitioning approaches can have attractive theoretical properties (e.g. distribution-free test thresholds) and work well in low dimensions, however they are much less powerful than alternatives once the dimensionality increases (Gretton & Gyorfi, 2010).”
A low variance consistent test of relative dependency (2014, background): “The statistics for such tests are diverse, and include kernel measures of covariance [5, 19] and correlation [2, 3], distance covariances (which are instances of kernel tests) [18, 14], rankings [7], and space partitioning approaches [6, 12, 9].”
Characteristic Kernels and Infinitely Divisible Distributions (2014, background): “…al., 2008; McCalman et al., 2013), hypothesis tests (two sample test, Gretton et al. 2012, indepen- c©2014 Yu Nishiyama and Kenji Fukumizu. dence test, Gretton and Györfi 2010, conditional independence test, Fukumizu et al. 2008), Bayesian inference (conditional distributions, Song et al. 2009,…”
A Kernel Independence Test for Random Processes (2014, background): “…are independent and identically distributed, a number of non-parametric tests of independence have been developed (Feuerverger, 1993; Gretton et al., 2007; Székely et al., 2009; Gretton & Györfi, 2010), which determine whether the dependence measure value is statistically significant.”
DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model (2011, methodology): “Future works would include i) assessment of practical performance of statistical tests to detect violations of the model assumptions including tests of independence [36]; ii) implementation issues of our algorithm to improve the practical computational eﬃciency.”
Minimax optimal conditional independence testing (2020, background): “In an interesting paper, Györfy and Walk [16], extend the independence testing results of Gretton and Györfi [15] to the CI case, and propose strongly consistent nonparametric tests.”
Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions (2016, methodology): “…interest in any MMD-based algorithm, such as kernel two-sample tests (Gretton et al., 2007, 2012), HSIC independence tests (Gretton et al., 2008; Gretton and Gy¨orﬁ, 2010; Fukumizu et al., 2008), kernel density estimators (Sriperumbudur, 2016) and MMD-type GANs (Li et al., 2015; Dziugaite et…”
The Nonparametric Kernel Bayes Smoother (2016, methodology): “This embedding approach has several benefits over previous nonparametric methods: (i) closeness and similarity in the set of probability distributions is introduced via the RKHS norm, which is useful for various machine learning algorithms [12, 11, 9, 20, 30]; and (ii) estimation is relatively easy ”
Kernel-Based Methods for Hypothesis Testing: A Unified View (2013, unknown): “This leads naturally to the Hilbert Schmidt independence criterion (HSIC) [17], [56], which is the squared Hilbert-Schmidt norm of .”
Strongly consistent nonparametric tests of conditional independence (2012, methodology): “Devroye and Lugosi (2002), Biau and Györfi (2005), and Gretton and Györfi (2010) provide further discussion and references.”
Nonparametric independence testing via mutual information (2017, background): “Other test statistics include those based on partitioning the sample space (e.g. Gretton and Gy¨orﬁ, 2010; Heller et al., 2016).”
The exact equivalence of distance and kernel methods in hypothesis testing (2018, methodology): “The Hilbert-Schmidt independence criterion is a kernel-based method for testing independence and equally popular in related inference tasks [1, 2, 4, 6, 7, 26, 36].”
Energy statistics: A class of statistics based on distances (2013, background): “For other recent consistent tests of bivariate or multivariate independence see e.g. Feuerverger (1993), Gretton and Györfi (2010), and Gretton and Györfi (2012).”