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Title: Characteristic and Universal Tensor Product Kernels
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 the characteristic property of the tensor product kernel.  more » « less
Award ID(s):
1713011
NSF-PAR ID:
10069240
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of machine learning research
Volume:
18
ISSN:
1533-7928
Page Range / eLocation ID:
1-29
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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