Optimal Rates for Nonparametric Density Estimation under Communication Constraints
Statistics Theory
2021-07-22 v1 Data Structures and Algorithms
Information Theory
math.IT
Statistics Theory
Abstract
We consider density estimation for Besov spaces when each sample is quantized to only a limited number of bits. We provide a noninteractive adaptive estimator that exploits the sparsity of wavelet bases, along with a simulate-and-infer technique from parametric estimation under communication constraints. We show that our estimator is nearly rate-optimal by deriving minimax lower bounds that hold even when interactive protocols are allowed. Interestingly, while our wavelet-based estimator is almost rate-optimal for Sobolev spaces as well, it is unclear whether the standard Fourier basis, which arise naturally for those spaces, can be used to achieve the same performance.
Cite
@article{arxiv.2107.10078,
title = {Optimal Rates for Nonparametric Density Estimation under Communication Constraints},
author = {Jayadev Acharya and Clément L. Canonne and Aditya Vikram Singh and Himanshu Tyagi},
journal= {arXiv preprint arXiv:2107.10078},
year = {2021}
}