The Power of the Hybrid Model for Mean Estimation
The Power of the Hybrid Model for Mean Estimation
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DOI：
10.2478/popets-2020-0062
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发表时间：
2018-11
影响因子：
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通讯作者：
Yatharth Dubey;A. Korolova
中科院分区：
文献类型：
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作者：
Yatharth Dubey;A. Korolova
摘要：我们探讨了差分隐私（DP）混合模型的威力，其中一些用户希望获得 DP 本地模型的保证，而其他用户则满足于接受可信策展人模型的保证。特别是，我们研究了混合模型估计器的实用性，该估计器计算具有有限支持的任意实值分布的平均值。当管理者知道分布的方差时，我们设计了一个混合估计器，对于实际数据集和参数设置，它可以实现相对于自然基线的恒定因子改进。然后，我们分析地描述估计器的效用如何通过问题设置和参数选择进行参数化。当分布的方差未知时，我们设计一个启发式混合估计器并分析它与基线的比较。我们发现它通常比基线表现得更好，有时几乎与已知方差估计器一样好。然后，我们回答这样的问题：当用户的数据不是来自相同的分布，而是来自依赖于他们的信任模型偏好的分布时，我们的估计器的效用会受到怎样的影响。具体来说，我们研究了两组分布差异的影响，并表明在某些情况下，我们的估计量保持相当高的效用。然后，我们演示如何将我们的混合估计器作为子组件合并到更复杂、更高维度的应用中。最后，我们为由于群体之间的交互而出现的混合模型提出了一种新的隐私放大概念，并为我们的混合估计器得出相应的放大结果。
Abstract We explore the power of the hybrid model of differential privacy (DP), in which some users desire the guarantees of the local model of DP and others are content with receiving the trusted-curator model guarantees. In particular, we study the utility of hybrid model estimators that compute the mean of arbitrary realvalued distributions with bounded support. When the curator knows the distribution’s variance, we design a hybrid estimator that, for realistic datasets and parameter settings, achieves a constant factor improvement over natural baselines.We then analytically characterize how the estimator’s utility is parameterized by the problem setting and parameter choices. When the distribution’s variance is unknown, we design a heuristic hybrid estimator and analyze how it compares to the baselines. We find that it often performs better than the baselines, and sometimes almost as well as the known-variance estimator. We then answer the question of how our estimator’s utility is affected when users’ data are not drawn from the same distribution, but rather from distributions dependent on their trust model preference. Concretely, we examine the implications of the two groups’ distributions diverging and show that in some cases, our estimators maintain fairly high utility. We then demonstrate how our hybrid estimator can be incorporated as a sub-component in more complex, higher-dimensional applications. Finally, we propose a new privacy amplification notion for the hybrid model that emerges due to interaction between the groups, and derive corresponding amplification results for our hybrid estimators.