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 |
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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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