We consider the task of estimating sparse discrete distributions under local differential privacy  and communication constraints. Under local privacy constraints , we present a sample-optimal private-coin scheme that only sends a one-bit message per user. For communication constraints, we present a public-coin scheme based on random hashing functions , which we prove is optimal up to logarithmic factors. Our results show that the sample complexity only depends logarithmically on the ambient dimension, thus providing significant improvement in sample complexity under sparsity assumptions. Our lower bounds are based on a recently proposed chi-squared contraction method .
We consider the problem of estimating sparse discrete distributions under local differential privacy (LDP) and communication constraints. We characterize the sample complexity for sparse estimation under LDP constraints up to a constant factor and the sample complexity under communication constraints up to a logarithmic factor. Our upper bounds under LDP are based on the Hadamard Response, a private coin scheme that requires only one bit of communication per user. Under communication constraints, we propose public coin schemes based on random hashing functions . Our tight lower bounds are based on the recently proposed method of chi squared contractions .
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task
problem
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(LDP)
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Under local privacy constraints , we present a sample-optimal private-coin scheme that only sends a one-bit message
We characterize the sample complexity for sparse estimation under LDP constraints up to a constant factor and the sample complexity under communication constraints up to a logarithmic factor. Our upper bounds under LDP are based on the Hadamard Response, a private coin scheme that requires only one bit of communication
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For
Under
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present a public-coin scheme
propose public coin schemes
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, which we prove is optimal up to logarithmic factors. Our results show that the sample complexity only depends logarithmically on the ambient dimension, thus providing significant improvement in sample complexity under sparsity assumptions. Our
. Our tight
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a recently proposed chi-squared contraction method
the recently proposed method of chi squared contractions