TY - GEN
T1 - Hypothesis testing in the high privacy limit
AU - Liao, Jiachun
AU - Sankar, Lalitha
AU - Tan, Vincent Y F
AU - Calmon, Flavio P.
N1 - Funding Information:
This work is supported in part by the National Science Foundation under grants CCF-1350914 and CIF-1422358
Publisher Copyright:
© 2016 IEEE.
PY - 2017/2/10
Y1 - 2017/2/10
N2 - Binary hypothesis testing under the Neyman-Pearson formalism is a statistical inference framework for distinguishing data generated by two different source distributions. Privacy restrictions may require the curator of the data or the data respondents themselves to share data with the test only after applying a randomizing privacy mechanism. Using mutual information as the privacy metric and the relative entropy between the two distributions of the output (post-randomization) source classes as the utility metric (motivated by the Chernoff-Stein Lemma), this work focuses on finding an optimal mechanism that maximizes the chosen utility function while ensuring that the mutual information based leakage for both source distributions is bounded. Focusing on the high privacy regime, an Euclidean information-theoretic (E-IT) approximation to the tradeoff problem is presented. It is shown that the solution to the E-IT approximation is independent of the alphabet size and clarifies that a mutual information based privacy metric preserves the privacy of the source symbols in inverse proportion to their likelihood.
AB - Binary hypothesis testing under the Neyman-Pearson formalism is a statistical inference framework for distinguishing data generated by two different source distributions. Privacy restrictions may require the curator of the data or the data respondents themselves to share data with the test only after applying a randomizing privacy mechanism. Using mutual information as the privacy metric and the relative entropy between the two distributions of the output (post-randomization) source classes as the utility metric (motivated by the Chernoff-Stein Lemma), this work focuses on finding an optimal mechanism that maximizes the chosen utility function while ensuring that the mutual information based leakage for both source distributions is bounded. Focusing on the high privacy regime, an Euclidean information-theoretic (E-IT) approximation to the tradeoff problem is presented. It is shown that the solution to the E-IT approximation is independent of the alphabet size and clarifies that a mutual information based privacy metric preserves the privacy of the source symbols in inverse proportion to their likelihood.
KW - Binary hypothesis testing
KW - Euclidean information theory
KW - Privacy
UR - http://www.scopus.com/inward/record.url?scp=85015187588&partnerID=8YFLogxK
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U2 - 10.1109/ALLERTON.2016.7852293
DO - 10.1109/ALLERTON.2016.7852293
M3 - Conference contribution
AN - SCOPUS:85015187588
T3 - 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
SP - 649
EP - 656
BT - 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
Y2 - 27 September 2016 through 30 September 2016
ER -