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Optimal Rates for Nonparametric Density Estimation under Communication Constraints
Jayadev Acharya · Clement Canonne · Aditya Vikram Singh · Himanshu Tyagi

Tue Dec 07 08:30 AM -- 10:00 AM (PST) @

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.

Author Information

Jayadev Acharya (Cornell University)
Clement Canonne (University of Sydney)
Aditya Vikram Singh (Indian Institute of Science)
Himanshu Tyagi

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