Optimal Rates for Nonparametric Density Estimation under Communication Constraints

Acharya, J and Canonne, CL and Singh, AV and Tyagi, H (2021) Optimal Rates for Nonparametric Density Estimation under Communication Constraints. In: 35th Conference on Neural Information Processing Systems, NeurIPS 2021, 6 December 2021 through 14 December 2021, Virtual, Online, pp. 26754-26766.

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Abstract

We consider density estimation for Besov spaces when the estimator is restricted to use only a limited number of bits about each sample. We provide a noninteractive adaptive estimator which 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 minmax 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.

Item Type:	Conference Paper
Publication:	Advances in Neural Information Processing Systems
Publisher:	Neural information processing systems foundation
Additional Information:	The copyright for this article belongs to the Neural information processing systems foundation.
Keywords:	Banach spaces, Adaptive estimators; Besov spaces; Communication constraints; Density estimation; Low bound; Min-max; Nonparametric density estimation; Optimal rate; Parametric estimation; Wavelet basis, Sobolev spaces
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	27 Jun 2022 07:24
Last Modified:	27 Jun 2022 07:24
URI:	https://eprints.iisc.ac.in/id/eprint/73994

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