Differential privacy (DP) has become the gold standard for ensuring the privacy protection of machine learning and statistical algorithms in recent decades. A plethora of algorithms and methods have been developed to enhance the utility of DP algorithms while maintaining the same level of DP. However, these are often overly complex or computationally ineffective. We propose a novel approach focusing on denoising the output of the simple additive Gaussian mechanism by adopting the idea of \textit{empirical Bayes estimation}. We highlight that the empirical Bayes approach can reduce the mean-squared error solely by taking the output of the Gaussian mechanism as input. Our numerical studies show that this simple yet powerful approach can be applied to improve upon various statistical problems, including histogram release, principal component analysis, and linear regression, often outperforming existing private algorithms.

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