Differentially Private Covariance Revisited

Wei Dong; Yuting Liang; Ke Yi

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arXiv · 2205.14324

Differentially Private Covariance Revisited

Wei Dong·Yuting Liang·Ke Yi

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Abstract

In this paper, we present two new algorithms for covariance estimation under concentrated differential privacy (zCDP). The first algorithm achieves a Frobenius error of $\tilde{O}(d^{1/4}\sqrt{\mathrm{tr}}/\sqrt{n} + \sqrt{d}/n)$, where $\mathrm{tr}$ is the trace of the covariance matrix. By taking $\mathrm{tr}=1$, this also implies a worst-case error bound of $\tilde{O}(d^{1/4}/\sqrt{n})$, which improves the standard Gaussian mechanism's $\tilde{O}(d/n)$ for the regime $d>\widetilde{\Omega}(n^{2/3})$. Our second algorithm offers a tail-sensitive bound that could be much better on skewed data. The corresponding algorithms are also simple and efficient. Experimental results show that they offer significant improvements over prior work.

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Wei Dong, Yuting Liang, Ke Yi. 2022-05-28. Differentially Private Covariance Revisited. https://arxiv.org/abs/2205.14324

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