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 -