Data-Driven Nonparametric Existence and Association Problems
From MaRDI portal
Publication:4622526
DOI10.1109/TSP.2018.2875392zbMATH Open1414.62147arXiv1711.08420OpenAlexW2768434904WikidataQ128981715 ScholiaQ128981715MaRDI QIDQ4622526
Yixian Liu, Yingbin Liang, Shuguang Cui
Publication date: 12 February 2019
Published in: IEEE Transactions on Signal Processing (Search for Journal in Brave)
Abstract: We investigate two closely related nonparametric hypothesis testing problems. In the first problem (i.e., the existence problem), we test whether a testing data stream is generated by one of a set of composite distributions. In the second problem (i.e., the association problem), we test which one of the multiple distributions generates a testing data stream. We assume that some distributions in the set are unknown with only training sequences generated by the corresponding distributions are available. For both problems, we construct the generalized likelihood (GL) tests, and characterize the error exponents of the maximum error probabilities. For the existence problem, we show that the error exponent is mainly captured by the Chernoff information between the set of composite distributions and alternative distributions. For the association problem, we show that the error exponent is captured by the minimum Chernoff information between each pair of distributions as well as the KL divergences between the approximated distributions (via training sequences) and the true distributions. We also show that the ratio between the lengths of training and testing sequences plays an important role in determining the error decay rate.
Full work available at URL: https://arxiv.org/abs/1711.08420
This page was built for publication: Data-Driven Nonparametric Existence and Association Problems
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4622526)
