Characteristic and Universal Tensor Product Kernels
Characteristic and Universal Tensor Product Kernels
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DOI：
10.13140/rg.2.2.27112.37120
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发表时间：
2017-08
期刊：
影响因子：
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通讯作者：
Z. Szabó;Bharath K. Sriperumbudur
中科院分区：
文献类型：
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作者：
Z. Szabó;Bharath K. Sriperumbudur
最大平均差异（MMD），也称为能量距离或N-距离在统计学和希尔伯特-施密特独立准则（HSIC），特别是距离协方差在统计学中，是最流行和最成功的方法来量化的差异和随机变量的独立性，分别。由于它们基于内核的基础，MMD和HSIC适用于各种各样的领域。尽管他们取得了巨大的成功，相当少的是知道什么时候HSIC的特点独立性和MMD与张量积核可以歧视概率分布。在本文中，我们回答了这些问题，通过研究各种概念的特征性质的张量积核。
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.