A Kernel Statistical Test of Independence

By Arthur Gretton, Kenji Fukumizu, Choon Hui Teo, Le Song, Bernhard Schölkopf, Alex Smola. 2007

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Citations in the corpus

Gradient-Based Neural DAG Learning (2019, methodology): “based on HSIC [15]) to recover the underlying CPDAG.”
f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization (2016, methodology): “The advantage of VAEs is in the encoder model which allows efficient inference from observation to latent representation and overall they are a compelling alternative to f -GANs and recent work has studied combinations of the two approaches [23] As an alternative to the GAN training objective the wo”
Causal Discovery from Heterogeneous/Nonstationary Data (2019, methodology): “In this section, we extend HSIC to measure the dependence between causal modules, based on which we determine causal directions.”
The hardness of conditional independence testing and the generalised covariance measure (2018, methodology): “We also compare to a test that performs the same regression as GCM, but then tests for independence between the residuals, rather than vanishing correlation, using HSIC [25].”
Behind Distribution Shift: Mining Driving Forces of Changes and Causal Arrows (2017, methodology): “|X) can be estimated by extending the Hilbert-Schmidt Independence Criterion (HSIC) [3]. a) HSIC: Given a set of observations {(u1, v1), (u2, v2), ..., (uN , vN )} for variables U and V , respectively, HSIC provides a statistic for testing their statistical independence as well as a measure of depen”
Invariant Causal Prediction for Sequential Data (2017, methodology): “A framework that connects stability (or invariance) to causality has been recently formulated by Peters, Bühlmann, and Meinshausen (2016) under the name invariant causal prediction which we will summarize next.”
The Arrow of Time in Multivariate Time Series (2016, methodology): “We ﬁrst report a consistency results for HSIC for time dependent data (Chwialkowski and Gretton, 2014).”
Kernel‐based tests for joint independence (2016, methodology): “…tests date back to Feuerverger (1993) and Romano (1986) and have more recently received considerable attention by using kernel-based methods (Gretton et al., 2005, 2007), and other related approaches for estimating or testing pairwise (in)dependence including distance correlations (Székely…”
Kernel-based Conditional Independence Test and Application in Causal Discovery (2011, methodology): “This unconditional independence testing method is closely related to the one based on the Hilbert-Schmidt independence criterion (HSIC) proposed by Gretton et al. (2008). Actually the defined statistics (our statistic TUI and HSICb in Gretton et al.”
Bayesian Learning of Kernel Embeddings (2016, methodology): “The empirical versions of MMD and HSIC are used as test statistics for the two-sample ( H 0 : P = Q vs.”
Minimax Estimation of Kernel Mean Embeddings (2016, methodology): “, 2007, 2012), kernel independence and conditional independence tests (Gretton et al., 2008; Fukumizu et al., 2008), covariate-shift (Smola et al.”
A Kernel Test of Goodness of Fit (2016, methodology): “The approach is a natural extension to goodness-of-fit testing of the earlier kernel two-sample tests (Gretton et al., 2012) and independence tests (Gretton et al., 2007), which are based on the maximum mean discrepancy, an integral probability metric.”
A Wild Bootstrap for Degenerate Kernel Tests (2014, methodology): “Following symmetrisation, it is shown in [17, 8] that the empirical HSIC can be written as a degree four V -statistic with core given by”
A low variance consistent test of relative dependency (2014, background): “The statistics for such tests are diverse, and include kernel measures of covariance (Gretton et al., 2008; Zhang et al., 2011) and correlation (Dauxois & Nkiet, 1998; Fukumizu et al.”
Nonparametric Independence Testing for Small Sample Sizes (2014, methodology): “detect dependence (some of them were used in previous papers on independence testing like [Gretton et al., 2007] and [Chwialkowski and Gretton, 2014]).”
Kernel Mean Shrinkage Estimators (2014, methodology): “…appealing to many algorithms in modern kernel methods, namely, two-sample testing via maximum mean discrepancy (MMD) (Gretton et al., 2007, 2012), kernel independence tests (Gretton et al., 2008), Hilbert space embedding of HMMs (Song et al., 2010), and kernel Bayes rule (Fukumizu et al., 2011).”