使用 Misra-Gries 草图实现更好的差分隐私近似直方图与重击者
Better Differentially Private Approximate Histograms and Heavy Hitters using the Misra-Gries Sketch
AI总结：
针对流式近似直方图与重击者的差分隐私发布，本文改进 Misra-Gries 草图机制，使噪声不随草图规模线性增长，并支持用户贡献多个不同元素。
摘要：
我们研究在元素流中计算差分隐私近似直方图和重击者的问题。在非隐私环境中，这通常使用 Misra 和 Gries 提出的草图完成 [Science of Computer Programming, 1982]。Chan、Li、Shi 和 Xu [PETS 2012] 描述了 Misra-Gries 草图的一个差分隐私版本，但其加入的噪声量可能很大，并且随草图大小线性增长；草图越精确，该方法必须加入的噪声就越多。我们提出一种在 (ε,δ)-差分隐私下发布 Misra-Gries 草图的更好机制。它加入的噪声幅度与草图大小无关；事实上，由噪声导致的最大误差在常数因子意义下与隐私非流式环境中已知的最佳结果相同。我们的机制简单且可能具有实用性。我们还给出了一个简单的 Misra-Gries 草图后处理步骤，该步骤不会增加最坏情况误差保证。只需以小于非流式环境两倍的幅度向这一新草图加入噪声即可。这改进了此前 ε-差分隐私的结果，在该结果中噪声随草图大小线性增长。最后，我们考虑用户可贡献多个不同元素的一般环境。我们提出一种新草图，其最大误差与 Misra-Gries 草图相匹配。在此环境中的许多参数下，我们的草图能够在 (ε,δ)-差分隐私下以更少噪声发布。
英文摘要：
We consider the problem of computing differentially private approximate histograms and heavy hitters in a stream of elements. In the non-private setting, this is often done using the sketch of Misra and Gries [Science of Computer Programming, 1982]. Chan, Li, Shi, and Xu [PETS 2012] describe a differentially private version of the Misra-Gries sketch, but the amount of noise it adds can be large and scales linearly with the size of the sketch; the more accurate the sketch is, the more noise this approach has to add. We present a better mechanism for releasing a Misra-Gries sketch under $(\varepsilon,δ)$-differential privacy. It adds noise with magnitude independent of the size of the sketch; in fact, the maximum error coming from the noise is the same as the best known in the private non-streaming setting, up to a constant factor. Our mechanism is simple and likely to be practical. We also give a simple post-processing step of the Misra-Gries sketch that does not increase the worst-case error guarantee. It is sufficient to add noise to this new sketch with less than twice the magnitude of the non-streaming setting. This improves on the previous result for $\varepsilon$-differential privacy where the noise scales linearly to the size of the sketch. Finally, we consider a general setting where users can contribute multiple distinct elements. We present a new sketch with maximum error matching the Misra-Gries sketch. For many parameters in this setting our sketch can be released with less noise under $(\varepsilon, δ)$-differential privacy.
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