A Kernel Approach to Comparing Distributions

By Arthur Gretton, Karsten M. Borgwardt, Malte J. Rasch, Bernhard Schölkopf, Alex Smola. 2007

60 citations recorded by the source corpus.

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Citations in the corpus

MOPO: Model-based Offline Policy Optimization (2020, background): “This is implemented as a constraint on the average MMD [22] between π ( · | s ) and a generative model that approximates π B ( · | s ) .”
Behavior Regularized Offline Reinforcement Learning (2019, methodology): “BEAR measures divergence from the behavior policy using kernel MMD (Gretton et al., 2007): where K is a kernel function.”
Generalizing from Several Related Classification Tasks to a New Unlabeled Sample (2011, unknown): “If P̂X and P̂ ′X are based on the samples X1, . . . , Xn and X ′1, . . . , X ′ n′ , then 〈 Ψ(P̂X),Ψ(P̂ ′X) 〉 = 〈 1 n n∑ i=1 k′X(Xi, ·), 1 n′ n′∑ j=1 k′X(X ′ j , ·) 〉 = 1 nn′ n∑ i=1 n′∑ j=1 k′X(Xi, X ′ j).”
A Kernel Two-Sample Test (2012, methodology): “Note that we use a tighter bias bound than Gretton et al. (2007a). requires symmetrization by means of aghost sample, that is, a second set of observations drawn from the same distribution.”
Domain Generalization by Marginal Transfer Learning (2017, unknown): “We deﬁne the kernel mean embedding Ψ : P X → H k X : (5) This mapping has been studied in the framework of “characteristic kernels” (Gretton et al., 2007a), and it has been proved that universality of k X implies injectivity of Ψ (Gretton et al., 2007b; Sriperumbudur et al., 2010).”
Mean Map Kernel Methods for Semisupervised Cloud Classification (2010, unknown): “(10) The concept of the mean map has been recently extended and led to a full family of kernel methods known as mean kernels, which has mainly been used for the comparison of distributions in the kernel space [52], [53].”