Gaussian Approximation of Quantization Error for Estimation From Compressed Data

作     者：Kipnis, Alon Reeves, Galen 

作者机构：Stanford Univ Dept Stat Stanford CA 94305 USA Duke Univ Dept Elect & Comp Engn Durham NC 27708 USA Duke Univ Dept Stat Sci Durham NC 27708 USA 

出 版 物：《IEEE TRANSACTIONS ON INFORMATION THEORY》 (IEEE信息论汇刊)

年 卷 期：2021年第67卷第8期

页      面：5562-5579页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Koret Foundation NSF Division of Computing and Communication Foundations Direct For Computer & Info Scie & Enginr Funding Source: National Science Foundation 

主　　题：Lossy source coding spherical coding Gaussian noise parameter estimation indirect source coding sparse regression approximate message passing 

摘      要：We consider the distributional connection between the lossy compressed representation of a high-dimensional signal X using a random spherical code and the observation of X under an additive white Gaussian noise (AWGN). We show that the Wasserstein distance between a bitrate-R compressed version of X and its observation under an AWGN-channel of signa-to-noise ratio 2(2R) - 1 is bounded in the problem dimension. We utilize this fact to connect the risk of an estimator based on the compressed version of X to the risk attained by the same estimator when fed the AWGN-corrupted version of X. We demonstrate the usefulness of this connection by deriving various novel results for inference problems under compression constraints, including minimax estimation, sparse regression, compressed sensing, and universality of linear estimation in remote source coding.