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.

翻译：我们考虑了在地方差异隐私(LDP)和通信限制下估计分散分散分散分布的问题。我们把根据当地差异隐私(LDP)和通信限制(直至对数因素)进行稀少估计的抽样复杂性定性到一个不变因素,把通信限制(直至对数因素)的抽样复杂性定性到一个不变因素。我们根据当地差异隐私(LDP)和通信限制(LDP)进行的上限是基于Hadamard反应(Hadamard Response),这是一种只要求每个用户只需要一点通信的私人硬币计划。在通信限制下,我们提出基于随机散列功能的公共硬币计划。我们紧凑的下限是基于最近提出的黑白收缩方法。