Characteristic and Universal Tensor Product Kernels

Abstract : Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches to quantify the difference and independence of random variables, respectively. Thanks to their kernel-based foundations, MMD and HSIC are applicable on a wide variety of domains. Despite their tremendous success, quite little is known about when HSIC characterizes independence and when MMD with tensor product kernel can discriminate probability distributions. In this paper, we answer these questions by studying various notions of characteristic property of the tensor product kernel.
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[Research Report] École Polytechnique; Pennsylvania State University. 2018
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Soumis le : dimanche 13 mai 2018 - 14:00:16
Dernière modification le : jeudi 7 juin 2018 - 01:13:48

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  • HAL Id : hal-01585727, version 2
  • ARXIV : 1708.08157

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Zoltán Szabó, Bharath Sriperumbudur. Characteristic and Universal Tensor Product Kernels. [Research Report] École Polytechnique; Pennsylvania State University. 2018. 〈hal-01585727v2〉

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