A Fast, Consistent Kernel Two-Sample Test

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

247 citations recorded by the source corpus.

Subfields: Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Kernel‐based tests for joint independence (2016, methodology): “However, since h2 is a complicated function (see lemma D.8 in the on-line appendix) depending on the unknown distribution PX (as opposed to Gretton et al. (2009)) one must estimate h2, which means one would have to account additionally for that approximation.”
Kernel-based Conditional Independence Test and Application in Causal Discovery (2011, positive): “On the other hand, by extending the proof of Theorem 1 of Gretton et al. (2009), one can show that ∞ i,j =1 ( 1 n 2 λ x ,i λ y ,j − λ ∗ X,i λ ∗ Y,j ) z 2 ij → 0 in probability as n → ∞ .”
A Kernelized Stein Discrepancy for Goodness-of-fit Tests (2016, background): “As a consequence, a line of work has been devoted to approximating the critical values of (15), including bootstrap meth-ods (Arcones & Gine, 1992; Huskova & Janssen, 1993; Chwialkowski et al., 2014) and eigenvalue approximation (Gretton et al., 2009).”
Fast Two-Sample Testing with Analytic Representations of Probability Measures (2015, methodology): “…procedure, the eigenvalues of the joint gram matrix over samples from P and Q may be used in place of the population eigenvalues; the fastest quadratic-time MMD test uses a gamma approximation to the null distribution, which works well most of the times, but has no consistency guarantees [9].”
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, methodology): “…2010; 2011; Sejdinovic et al., 2013) and successful applications including biological data test (Borgwardt et al., 2006), data integration and attribute matching (Gretton et al., 2009), outlier detection, data classifiability (Sriperumbudur et al., 2009), domain adaption (Gong et al., 2013), etc.”
Testing Hypotheses by Regularized Maximum Mean Discrepancy (2013, methodology): “In comparison, the bootstrap resampling and the eigen-spectrum of the gram matrix are more consistent estimates with computational cost of O(n(2)), where n is the number of samples [11].”
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): “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 product of the marginals.”
Large-scale kernel methods for independence testing (2016, methodology): “The spectral approach (Gretton et al. 2009; Zhang et al. 2011) requires that we first calculate the centred Grammatrices K̃ X = H K X H and K̃Y = H KY H for the chosen kernel kX and kY .”
Linear-Time Learning on Distributions with Approximate Kernel Embeddings (2015, background): “Our JS and Hellinger embedding approximately match the histogram JS embedding in accuracy here, while our TV embedding beats histogram JS ; all outperform L 2 and MMD .”
B-test: A Non-parametric, Low Variance Kernel Two-sample Test (2013, methodology): “Although setting B = n would lead to the lowest variance estimate of the MMD, computing sound thresholds for a given p-value is expensive, involving repeated bootstrap sampling [5, 12], or computing the eigenvalues of a Gram matrix [7].”
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.”
A Permutation-Based Kernel Conditional Independence Test (2014, background): “two again, and then (2) the test statistic is recomputed between the shuffled samples (Gretton et al., 2009).”
Kernel-Based Methods for Hypothesis Testing: A Unified View (2013, unknown): “For instance, the so-called maximum mean discrepancy (MMD) test statistic [43], [44]”
Structured Time Series Analysis for Human Action Segmentation and Recognition (2014, methodology): “Besides the differences on temporal segmentation and transfer learning, our alignment step uses manifold learning to infer the latent “completion” variable, while [21], [22] use it to build the generative model.”
Learning Deep Kernels for Non-Parametric Two-Sample Tests (2020, background): “…central limit theorem holds (Serﬂing, 1980, Section 5.5.1): Although it is possible to construct a test based on directly estimating this null distribution (Gretton et al., 2009), it is both simpler and, if implemented carefully, faster (Suther-land et al., 2017) to instead use a permutation test.”