TY - GEN
T1 - A Variational Formula for Infinity-Rényi Divergence with Applications to Information Leakage
AU - Kurri, Gowtham R.
AU - Kosut, Oliver
AU - Sankar, Lalitha
N1 - Funding Information:
The authors are with the School of Electrical, Computer and Energy Engineering at Arizona State University. Email: gkurri@asu.edu, okosut@asu.edu, lalithasankar@asu.edu This work is supported in part by NSF grants CIF-1901243, CIF-1815361, CIF-2007688, CIF-2134256, and CIF-2031799.
Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - We present a variational characterization for the Rényi divergence of order infinity. Our characterization is related to guessing: the objective functional is a ratio of maximal expected values of a gain function applied to the probability of correctly guessing an unknown random variable. An important aspect of our variational characterization is that it remains agnostic to the particular gain function considered, as long as it satisfies some regularity conditions. Also, we define two variants of a tunable measure of information leakage, the maximal αleakage, and obtain closed-form expressions for these information measures by leveraging our variational characterization.
AB - We present a variational characterization for the Rényi divergence of order infinity. Our characterization is related to guessing: the objective functional is a ratio of maximal expected values of a gain function applied to the probability of correctly guessing an unknown random variable. An important aspect of our variational characterization is that it remains agnostic to the particular gain function considered, as long as it satisfies some regularity conditions. Also, we define two variants of a tunable measure of information leakage, the maximal αleakage, and obtain closed-form expressions for these information measures by leveraging our variational characterization.
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U2 - 10.1109/ISIT50566.2022.9834358
DO - 10.1109/ISIT50566.2022.9834358
M3 - Conference contribution
AN - SCOPUS:85136281933
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2493
EP - 2498
BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022
Y2 - 26 June 2022 through 1 July 2022
ER -