TY - CONF
T1 - Universal hypothesis testing with kernels
T2 - 22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019
AU - Zhu, Shengyu
AU - Chen, Biao
AU - Yang, Pengfei
AU - Chen, Zhitang
N1 - Funding Information:
The authors are grateful to the anonymous reviewers for valuable comments and suggestions. The work of BC was supported in part by the U.S. National Science Foundation under grant CNS-1731237 and by the U.S. Air Force Office of Scientific Research under grant FA9550-16-1-0077. Part of this work was done when SZ and PY were students at Syracuse University.
Publisher Copyright:
© Copyright 2019 by the author(s).
PY - 2020
Y1 - 2020
N2 - We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum rate subject to a constant level constraint on the type-I error probability. We show that two classes of Maximum Mean Discrepancy (MMD) based tests attain this optimality on Rd, while the quadratic-time Kernel Stein Discrepancy (KSD) based tests achieve the maximum exponential decay rate under a relaxed level constraint. Under the same performance metric, we proceed to show that the quadratic-time MMD based two-sample tests are also optimal for general two-sample problems, provided that kernels are bounded continuous and characteristic. Key to our approach are Sanov's theorem from large deviation theory and the weak metrizable properties of the MMD and KSD.
AB - We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum rate subject to a constant level constraint on the type-I error probability. We show that two classes of Maximum Mean Discrepancy (MMD) based tests attain this optimality on Rd, while the quadratic-time Kernel Stein Discrepancy (KSD) based tests achieve the maximum exponential decay rate under a relaxed level constraint. Under the same performance metric, we proceed to show that the quadratic-time MMD based two-sample tests are also optimal for general two-sample problems, provided that kernels are bounded continuous and characteristic. Key to our approach are Sanov's theorem from large deviation theory and the weak metrizable properties of the MMD and KSD.
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M3 - Paper
AN - SCOPUS:85085043735
Y2 - 16 April 2019 through 18 April 2019
ER -