TY - JOUR
T1 - Characteristic and universal tensor product kernels
AU - Szabó, Zoltán
AU - Sriperumbudur, Bharath K.
N1 - Funding Information:
The authors profusely thank Ingo Steinwart for fascinating discussions on topics related to the paper and for contributing to Remark 7. The authors also thank the anonymous reviewers for their constructive comments that improved the manuscript. A part of the work was carried out while BKS was visiting ZSz at CMAP, École Polytechnique. BKS is supported by NSF-DMS-1713011 and also thanks CMAP and DSI for their generous support. ZSz is highly grateful for the Greek hospitality around the Aegean Sea; it greatly contributed to the development of the induction arguments.
Publisher Copyright:
© 2018 Zoltán Szabó and Bharath K. Sriperumbudur.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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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M3 - Article
AN - SCOPUS:85053693056
SN - 1532-4435
VL - 18
SP - 1
EP - 29
JO - Journal of Machine Learning Research
JF - Journal of Machine Learning Research
ER -