TY - GEN
T1 - Communication Complexity of Two-party Nonparametric Global Density Estimation
AU - Liu, Jingbo
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - Consider the problem of nonparametric estimation of an unknown β -Hölder smooth density function pXY with compact support, where X and Y are both d dimensional. An infinite sequence of i.i.d. samples Xi, Yi) are generated according to this distribution, and two terminals observe (Xi) and Yi), respectively. They are allowed to exchange $k$ bits either in oneway or interactively in order for Bob to estimate the unknown density. We show that the minimax mean integrated square risk is order (\frack{\log k})-\frac{β}{d+β}} for one-way protocols, and between (\frack{\log k})-\frac{β}{d+β} and k(\frack{\log k})-\frac{β}{d+β} for interactive protocols. These rates are different from the case of pointwise density estimation which we recently determined in another work. The interactive lower bound in this work used, among other things, a recent result of Ordentlich and Polyanskiy regarding the optimality of binary inputs in certain optimizations related to the strong data processing constant.
AB - Consider the problem of nonparametric estimation of an unknown β -Hölder smooth density function pXY with compact support, where X and Y are both d dimensional. An infinite sequence of i.i.d. samples Xi, Yi) are generated according to this distribution, and two terminals observe (Xi) and Yi), respectively. They are allowed to exchange $k$ bits either in oneway or interactively in order for Bob to estimate the unknown density. We show that the minimax mean integrated square risk is order (\frack{\log k})-\frac{β}{d+β}} for one-way protocols, and between (\frack{\log k})-\frac{β}{d+β} and k(\frack{\log k})-\frac{β}{d+β} for interactive protocols. These rates are different from the case of pointwise density estimation which we recently determined in another work. The interactive lower bound in this work used, among other things, a recent result of Ordentlich and Polyanskiy regarding the optimality of binary inputs in certain optimizations related to the strong data processing constant.
UR - http://www.scopus.com/inward/record.url?scp=85126904247&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85126904247&partnerID=8YFLogxK
U2 - 10.1109/CISS53076.2022.9751150
DO - 10.1109/CISS53076.2022.9751150
M3 - Conference contribution
AN - SCOPUS:85126904247
T3 - 2022 56th Annual Conference on Information Sciences and Systems, CISS 2022
SP - 292
EP - 297
BT - 2022 56th Annual Conference on Information Sciences and Systems, CISS 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 56th Annual Conference on Information Sciences and Systems, CISS 2022
Y2 - 9 March 2022 through 11 March 2022
ER -