Robust Mean Estimation under Quantization

Parameter estimation under quantization is a fundamental problem at the intersection of statistics [12], signal processing [14], and machine learning [4]. Quantization is of fundamental importance in these fields, mainly due to its role in reducing memory and storage costs. In distributed learning, quantization plays a key role to reduce the cost of communication between data servers, where the central server has to estimate a parameter from the quantized data sent by the data servers. As pointed out in [17], quantization also contributes to the recent paradigm of data privacy, since the quantized sample preserves sensitive information: the estimator only have access to bits, which reduces the chance to leak sensitive information. In this work, we consider what is arguably the most fundamental parameter estimation task: the estimation of the mean of a random vector X from n i.i.d.