TY - GEN
T1 - Estimation of KL divergence between large-alphabet distributions
AU - Bu, Yuheng
AU - Zou, Shaofeng
AU - Liang, Yingbin
AU - Veeravalli, Venugopal V.
N1 - Funding Information:
The work of Y. Bu and V. V. Veeravalli was supported by the Air Force Office of Scientific Research (AFOSR) under the Grant FA9550-10-1-0458, and by the National Science Foundation under Grant NSF 11-11342, through the University of Illinois at Urbana-Champaign. The work of S. Zou and Y. Liang was supported by an NSF CAREER Award under Grant CCF-10-26565
Publisher Copyright:
© 2016 IEEE.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - The problem of estimating the KL divergence between two unknown distributions is studied. The alphabet size k of the distributions can scale to infinity. The estimation is based on m and n independent samples respectively drawn from the two distributions. It is first shown that there does not exist any consistent estimator to guarantee asymptotic small worst-case quadratic risk over the set of all pairs of distributions. A restricted set that contains pairs of distributions with bounded ratio F(k) is further considered. An augmented plug-in estimator is proposed, and is shown to be consistent if and only if m = ω(k V log2(F(k)) and n = ω(kF(k)). Furthermore, if F(k) ≥ log2k and log2(F(k)) = o(k), it is shown that any consistent estimator must satisfy the necessary conditions: m = ω( k/log k V log2(F(k)) and n = ω( kF(k)/log k).
AB - The problem of estimating the KL divergence between two unknown distributions is studied. The alphabet size k of the distributions can scale to infinity. The estimation is based on m and n independent samples respectively drawn from the two distributions. It is first shown that there does not exist any consistent estimator to guarantee asymptotic small worst-case quadratic risk over the set of all pairs of distributions. A restricted set that contains pairs of distributions with bounded ratio F(k) is further considered. An augmented plug-in estimator is proposed, and is shown to be consistent if and only if m = ω(k V log2(F(k)) and n = ω(kF(k)). Furthermore, if F(k) ≥ log2k and log2(F(k)) = o(k), it is shown that any consistent estimator must satisfy the necessary conditions: m = ω( k/log k V log2(F(k)) and n = ω( kF(k)/log k).
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U2 - 10.1109/ISIT.2016.7541473
DO - 10.1109/ISIT.2016.7541473
M3 - Conference contribution
AN - SCOPUS:84985993750
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1118
EP - 1122
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Y2 - 10 July 2016 through 15 July 2016
ER -