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Privacy-preserving parametric inference: A case for robust statistics
Journal of the American Statistical Association ( IF 3.0 ) Pub Date : 2020-10-16 , DOI: 10.1080/01621459.2019.1700130
Marco Avella-Medina 1
Affiliation  

Differential privacy is a cryptographically-motivated approach to privacy that has become a very active field of research over the last decade in theoretical computer science and machine learning. In this paradigm one assumes there is a trusted curator who holds the data of individuals in a database and the goal of privacy is to simultaneously protect individual data while allowing the release of global characteristics of the database. In this setting we introduce a general framework for parametric inference with differential privacy guarantees. We first obtain differentially private estimators based on bounded influence M-estimators by leveraging their gross-error sensitivity in the calibration of a noise term added to them in order to ensure privacy. We then show how a similar construction can also be applied to construct differentially private test statistics analogous to the Wald, score and likelihood ratio tests. We provide statistical guarantees for all our proposals via an asymptotic analysis. An interesting consequence of our results is to further clarify the connection between differential privacy and robust statistics. In particular, we demonstrate that differential privacy is a weaker stability requirement than infinitesimal robustness, and show that robust M-estimators can be easily randomized in order to guarantee both differential privacy and robustness towards the presence of contaminated data. We illustrate our results both on simulated and real data.

中文翻译:

隐私保护参数推理:稳健统计的一个案例

差分隐私是一种以密码学为动机的隐私方法,在过去十年中,它已成为理论计算机科学和机器学习中一个非常活跃的研究领域。在这种范式中,假设有一个受信任的策展人将个人数据保存在数据库中,隐私的目标是同时保护个人数据,同时允许发布数据库的全局特征。在此设置中,我们引入了具有差异隐私保证的参数推理的通用框架。我们首先通过在添加到它们中的噪声项的校准中利用它们的总误差敏感性来获得基于有界影响 M 估计器的差分私有估计器,以确保隐私。然后,我们展示了如何应用类似的构造来构建类似于 Wald、分数和似然比测试的差异化私有测试统计量。我们通过渐近分析为所有提案提供统计保证。我们结果的一个有趣结果是进一步阐明了差异隐私和稳健统计之间的联系。特别是,我们证明了差分隐私是比无穷小的稳健性更弱的稳定性要求,并表明稳健的 M 估计器可以很容易地随机化,以保证差分隐私和对存在污染数据的稳健性。我们在模拟和真实数据上说明了我们的结果。我们通过渐近分析为所有提案提供统计保证。我们结果的一个有趣结果是进一步阐明了差异隐私和稳健统计之间的联系。特别是,我们证明了差分隐私是比无穷小的鲁棒性更弱的稳定性要求,并表明鲁棒 M 估计器可以很容易地随机化,以保证差分隐私和对存在污染数据的鲁棒性。我们在模拟和真实数据上说明了我们的结果。我们通过渐近分析为所有提案提供统计保证。我们结果的一个有趣结果是进一步阐明了差异隐私和稳健统计之间的联系。特别是,我们证明了差分隐私是比无穷小的鲁棒性更弱的稳定性要求,并表明鲁棒 M 估计器可以很容易地随机化,以保证差分隐私和对存在污染数据的鲁棒性。我们在模拟和真实数据上说明了我们的结果。并表明鲁棒的 M 估计器可以很容易地随机化,以保证差异隐私和对存在污染数据的鲁棒性。我们在模拟和真实数据上说明了我们的结果。并表明鲁棒的 M 估计器可以很容易地随机化,以保证差异隐私和对存在污染数据的鲁棒性。我们在模拟和真实数据上说明了我们的结果。
更新日期:2020-10-16
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