Kernel Measures of Conditional Dependence

By Kenji Fukumizu, Arthur Gretton, Xiaohai Sun, Bernhard Schölkopf. 2007

683 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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In Probabilistic & Bayesian Methods

Citations in the corpus

Improved Techniques for Training GANs (2016, neutral): “3.1, is similar in spirit to approaches that use maximum mean discrepancy [7, 8, 9] to train generator networks [10, 11].”
Differentiable Causal Discovery from Interventional Data (2020, methodology): “Several constraint-based methods use kernel-based conditional independence tests [50, 12], which scale poorly with the number of examples.”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “…in many applications, namely, clustering (Jegelka et al. 2009), density estimation (Song et al. 2007a; 2008), (conditional) independence tests (Fukumizu et al. 2008, Doran et al. 2014, Chwialkowski and Gretton 2014), causal discovery (Sgouritsa et al. 2013, Chen et al. 2014, Schölkopf et al.…”
Towards Causal Representation Learning (2021, positive): “progress in (conditional) independence testing heavily relies on kernel function classes to represent probability distributions in reproducing kernel Hilbert spaces [90, 91, 73, 278, 60, 191, 42].”
Causality for Machine Learning (2019, methodology): “Recent progress in (conditional) independence testing heavily relies on kernel function classes to represent probability distributions in reproducing kernel Hilbert spaces (Gretton et al., 2005a,b; Fukumizu et al., 2008; Zhang et al., 2011; Pfister et al., 2018b; Chalupka et al., 2018).”
The hardness of conditional independence testing and the generalised covariance measure (2018, background): “[24] extend this idea to conditional independence testing.”
Fast Conditional Independence Test for Vector Variables with Large Sample Sizes (2018, methodology): “Here we consider six methods we are aware of for comparison: The Conditional Hilbert-Schmidt Independence Criterion (CHSIC) [Fukumizu et al., 2008] maps the data into a RKHS.”
Invariant Causal Prediction for Nonlinear Models (2017, methodology): “Use a kernel conditional independence test for Y ⊥⊥ E | X S (Fukumizu et al., 2008; Zhang et al., 2011).”
Kernel‐based tests for joint independence (2016, methodology): “A kernel is called characteristic if the mean embedding Π is injective (see Fukumizu et al. (2007)).”
Identifiability of Causal Graphs using Functional Models (2011, neutral): “[2009] and as a test either partial correlation (PCcorr) or “conditional HSIC” (PCHSIC) proposed by Fukumizu et al. [2008] with 500 bootstrap samples to generate the null distribution.”
Kernel-based Conditional Independence Test and Application in Causal Discovery (2011, methodology): “To get a test, one has to combine this conditional dependence measure with local bootstrap, or local permutation, which is used to determine the rejector region (Fukumizu et al., 2008; Tillman et al., 2009).”
Minimax Estimation of Kernel Mean Embeddings (2016, methodology): “…include kernel two-sample testing (Gretton et al., 2007, 2012), kernel independence and conditional independence tests (Gretton et al., 2008; Fukumizu et al., 2008), covariate-shift (Smola et al., 2007), density estimation (Sriperumbudur, 2011), feature selection (Song et al., 2012), causal…”
A Test of Relative Similarity For Model Selection in Generative Models (2015, background): “The maximum mean discrepancy is a metric on the space of probability distirbutions when a characteristic kernel is used (Fukumizu et al., 2008; Sriperumbudur et al., 2010), meaning that the distribution embeddings are unique for each probability measure.”
Computing functions of random variables via reproducing kernel Hilbert space representations (2015, neutral): “Wecanmapconditionaldistributionsandper-form Bayesian updates (Fukumizu et al. 2008, 2013; Zhang etal.2011),andwecanconnectkernelmapstoFourieroptics, leading to a physical realization as Fraunhofer diffraction (Harmeling et al. 2013).”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, background): “The justification for the name “independence criterion” stems from the following important result (Fukumizu et al., 2008, Theorem 3): Lemma 12 Whenever the product kernel k · l is characteristic (in the sense of (Fukumizu et al., 2008; Sriperumbudur et al., 2010)): HSICk,l(X,Y ) = 0 if and only if…”
A Wild Bootstrap for Degenerate Kernel Tests (2014, methodology): “Statistical tests based on distribution embeddings into reproducing kernel Hilbert spaces have been applied in many contexts, including two sample testing [19, 15, 31], tests of independence [17, 32, 4], tests of conditional independence [14, 32], and tests for higher order (Lancaster) interactions ”
On the Decreasing Power of Kernel and Distance Based Nonparametric Hypothesis Tests in High Dimensions (2014, methodology): “g problem) involve the use of test statistics based on quantities deﬁned in reproducing kernel Hilbert spaces (RKHSs), introduced in Gretton et al. (2012a); Eric et al. (2008); Gretton et al. (2005); Fukumizu et al. (2008), that are computed using kernels evaluated on pairs of points. A related set ”
Nonparametric Independence Testing for Small Sample Sizes (2014, background): “hrink towards several targets, including the zero and the identity matrix, and the expected kernel matrix. Large-scale Experiments. COCO, NOCCO and HSNIC are important alternatives to HSIC from [16], [17]. Our preliminary experiments suggest that shrinkage often improves and never worsens the power ”