TY - JOUR
T1 - Hypothesis Testing under Mutual Information Privacy Constraints in the High Privacy Regime
AU - Liao, Jiachun
AU - Sankar, Lalitha
AU - Tan, Vincent Y.F.
AU - Calmon, Flavio du Pin
N1 - Funding Information: Manuscript received April 26, 2017; revised September 13, 2017 and November 17, 2017; accepted November 18, 2017. Date of publication December 1, 2017; date of current version January 3, 2018. This work was supported in part by the National Science Foundation under Grant CCF-1350914 and Grant CIF-1422358 and in part by the Singapore Ministry of Education AcRF Tier 1 under Grant R-263-000-C54-114. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Tobias Oechtering. (Corresponding author: Jiachun Liao.) J. Liao and L. Sankar are with Arizona State University, Tempe, AZ 85281 USA (e-mail: [email protected]). Publisher Copyright: © 2005-2012 IEEE.
PY - 2018/4
Y1 - 2018/4
N2 - Hypothesis testing is a statistical inference framework for determining the true distribution among a set of possible distributions for a given data set. Privacy restrictions may require the curator of the data or the respondents themselves to share data with the test only after applying a randomizing privacy mechanism. This work considers mutual information (MI) as the privacy metric for measuring leakage. In addition, motivated by the Chernoff-Stein lemma, the relative entropy between pairs of distributions of the output (generated by the privacy mechanism) is chosen as the utility metric. For these metrics, the goal is to find the optimal privacy-utility tradeoff (PUT) and the corresponding optimal privacy mechanism for both binary and m -ary hypothesis testing. Focusing on the high privacy regime, Euclidean information-theoretic approximations of the binary and m -ary PUT problems are developed. The solutions for the approximation problems clarify that an MI-based privacy metric preserves the privacy of the source symbols in inverse proportion to their likelihoods.
AB - Hypothesis testing is a statistical inference framework for determining the true distribution among a set of possible distributions for a given data set. Privacy restrictions may require the curator of the data or the respondents themselves to share data with the test only after applying a randomizing privacy mechanism. This work considers mutual information (MI) as the privacy metric for measuring leakage. In addition, motivated by the Chernoff-Stein lemma, the relative entropy between pairs of distributions of the output (generated by the privacy mechanism) is chosen as the utility metric. For these metrics, the goal is to find the optimal privacy-utility tradeoff (PUT) and the corresponding optimal privacy mechanism for both binary and m -ary hypothesis testing. Focusing on the high privacy regime, Euclidean information-theoretic approximations of the binary and m -ary PUT problems are developed. The solutions for the approximation problems clarify that an MI-based privacy metric preserves the privacy of the source symbols in inverse proportion to their likelihoods.
KW - Hypothesis testing
KW - Rényi divergence
KW - euclidean information theory
KW - mutual information
KW - privacy mechanism
KW - privacy-guaranteed data publishing
KW - relative entropy
UR - https://www.scopus.com/pages/publications/85037672022
UR - https://www.scopus.com/pages/publications/85037672022#tab=citedBy
U2 - 10.1109/TIFS.2017.2779108
DO - 10.1109/TIFS.2017.2779108
M3 - Article
SN - 1556-6013
VL - 13
SP - 1058
EP - 1071
JO - IEEE Transactions on Information Forensics and Security
JF - IEEE Transactions on Information Forensics and Security
IS - 4
M1 - 8125176
ER -