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Kernel Measures of Conditional Dependence

著者: Kenji Fukumizu, Arthur Gretton, Xiaohai Sun, Bernhard Schölkopf - Conference on Neural Information Processing Systems, NeurIPS 2007 被引用: 684

We propose a new measure of conditional dependence of random variables, based on normalized cross-covariance operators on reproducing kernel Hilbert spaces. Unlike previous kernel dependence measures, the proposed criterion does not depend on the choice of kernel in the limit of infinite data, for a wide class of kernels. At the same time, it has a straightforward empirical estimate with good convergence behaviour. We discuss the theoretical properties of the measure, and demonstrate its application in experiments.

Joint measures andcross-covariance…Joint measures and cross-covariance operatorsFunctional analysisFunctional analysis10.1162/15324430276018525210.1162/153244302760185252Dimensionality Reductionfor Supervised Learning…Dimensionality Reduction for Supervised Learning with Reproducing Kernel Hilbert SpacesEstimating mutualinformationEstimating mutual informationKernel Methods forMeasuring IndependenceKernel Methods for Measuring IndependenceMeasuring StatisticalDependence with…Measuring Statistical Dependence with Hilbert-Schmidt NormsA Kernel Method for theTwo-Sample ProblemA Kernel Method for the Two-Sample ProblemA Kernel StatisticalTest of IndependenceA Kernel Statistical Test of IndependenceStatistical Consistencyof Kernel Canonical…Statistical Consistency of Kernel Canonical Correlation AnalysisA kernel-based causallearning algorithmA kernel-based causal learning algorithmKernel dimensionreduction in regressionKernel dimension reduction in regressionInjective Hilbert SpaceEmbeddings of…Injective Hilbert Space Embeddings of Probability MeasuresCharacteristic Kernelson Groups and SemigroupsCharacteristic Kernels on Groups and SemigroupsKernel dimensionreduction in regressionKernel dimension reduction in regressionKernel-based ConditionalIndependence Test and…Kernel-based Conditional Independence Test and Application in Causal DiscoveryKernel Bayes' RuleKernel Bayes' RuleEquivalence ofdistance-based and…Equivalence of distance-based and RKHS-based statistics in hypothesis testingKernel Bayes' rule:Bayesian inference with…Kernel Bayes' rule: Bayesian inference with positive definite kernelsA Kernel Test forThree-Variable…A Kernel Test for Three-Variable InteractionsFiltering withState-Observation…Filtering with State-Observation Examples via Kernel Monte Carlo FilterGaussian Processes andKernel Methods: A Revie…Gaussian Processes and Kernel Methods: A Review on Connections and EquivalencesKernel DistributionEmbeddings: Universal…Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on DistributionsKernel PartialCorrelation Coefficient…Kernel Partial Correlation Coefficient - a Measure of Conditional DependenceKernel Measures ofConditional DependenceKernel Measures of Conditional Dependence過去の参考文献中心の論文この論文を引用する論文古い新しい

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