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arXiv 1205.4697stat.MEcs.DS
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使用噪声度的推理:差分私有$β$模型和合成图

Inference using noisy degrees: Differentially private $β$-model and synthetic graphs

Vishesh Karwa, Aleksandra Slavković

摘要:

随机图的$β$ -模型是以度序列作为充分统计量的指数族模型。在本文中,我们贡献了三个关键结果。首先,我们的特点的条件,导致二次时间算法来检查存在的MLE的$β$模型,并表明,MLE从来没有存在的度分区$β$模型。其次,基于网络数据的隐私问题,我们推导了$β$模型参数的差分隐私估计,并证明了它是相容的和渐近正态分布的--它达到了与非隐私估计相同的收敛速度。我们提出了一个有效的算法的私人估计,可用于释放合成图。我们的技术也可以用来释放度分布和度分区准确和私人,并执行从噪声度产生的上下文而不是隐私的推断。我们评估建议的估计真实的图,并将其与目前的算法释放度分布,发现它做得更好。最后,我们的论文解决了目前的方法的一个基本问题,如何执行有效的统计推断隐私机制发布的数据的缺点,并奠定了基础,如何实现最佳和私人的统计推断的原则性方式建模的隐私机制,这些原则应适用于一类模型超出了$β$模型。

英文摘要:

The $β$-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. In this paper, we contribute three key results. First, we characterize conditions that lead to a quadratic time algorithm to check for the existence of MLE of the $β$-model, and show that the MLE never exists for the degree partition $β$-model. Second, motivated by privacy problems with network data, we derive a differentially private estimator of the parameters of $β$-model, and show it is consistent and asymptotically normally distributed - it achieves the same rate of convergence as the nonprivate estimator. We present an efficient algorithm for the private estimator that can be used to release synthetic graphs. Our techniques can also be used to release degree distributions and degree partitions accurately and privately, and to perform inference from noisy degrees arising from contexts other than privacy. We evaluate the proposed estimator on real graphs and compare it with a current algorithm for releasing degree distributions and find that it does significantly better. Finally, our paper addresses shortcomings of current approaches to a fundamental problem of how to perform valid statistical inference from data released by privacy mechanisms, and lays a foundational groundwork on how to achieve optimal and private statistical inference in a principled manner by modeling the privacy mechanism; these principles should be applicable to a class of models beyond the $β$-model.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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