Theoretical Foundations of Differentially Private Statistics

鉴于大型数据集的普遍存在，统计和机器学习被用于许多应用领域，以执行推理和预测。然而，许多数据集包含敏感的个人信息，因此确保这些程序的结果不会泄露这些私人信息至关重要。例如，假设我们正在对涉及HIV阳性个体的遗传数据进行假设检验。Homer等人的最新结果表明，在某些条件下，有可能重新识别参与此类研究的个体。当然，考虑到这种情况的社会耻辱性质，这将是对个人隐私的严重侵犯，从而阻止个人参与上述研究。本研究的目标是开发用于私人统计的方法和工具，并针对给定的任务回答以下中心问题：我们需要多少数据才能确保我们的任务解决方案不会侵犯用户的隐私？我将在理论和实践两个方向上同时推进。我计划以几种方式在我最近关于该领域基本问题的理论工作的基础上再接再厉。首先，我和我的团队将开发新的算法和分析，以解决更复杂和一般的任务。其次，我们将研究与大规模部署中实际应用的隐私设置直接匹配的隐私设置，并为这些设置设计时间和数据高效的算法。最后，我们将实验和调整理论算法，使代码是有效的真实的数据。虽然在隐私和统计方面进行了大量工作，但这项工作主要在两个方面有所不同：侧重于了解基本人口的特性，而不是特定的数据集，以及调查有限数据量的隐私成本，而不是数据量趋于无穷大的“渐近”设置。由于统计方法越来越普遍，隐私问题也越来越成为公共讨论的一个共同话题，因此，私营部门统计采用严格方法的重要性至关重要。特别地，由于最近的事件展示了大量用户数据的力量（例如，Facebook-剑桥分析公司数据丑闻），可能会制定大量新政策来防止此类事件再次发生。反过来，这将需要在几乎所有处理用户数据的公司中接受数据隐私培训的新的高素质人员-我的学生将准备填补的角色。

Given the ubiquity of large data sets, statistics and machine learning are used in numerous applications areas to perform inference and prediction. However, many data sets consist of sensitive personal information, and it is vital to make sure that the results of these procedures do not reveal this private information. As an example, suppose we are doing a hypothesis test on genetic data involving individuals who are HIV-positive. Recent results of Homer et al. have shown that, under certain conditions, it is possible to re-identify individuals who participated in such a study. Naturally, giving the socially-stigmatic nature of this condition, this would be a gross violation of individual privacy, thus discouraging individuals from participating in said research study. The goal of this research is to develop methods and tools for private statistics, and for a given task, answer the following central question: how much more data do we need to ensure that our solution to the task does not violate the privacy of the users? I will push forward simultaneously in both theoretical and practical directions. I plan to build on my recent theoretical work on fundamental problems in the area in a number of ways. First, my group and I will develop new algorithms and analysis in order to solve more complex and general tasks. Second, we will study privacy settings that directly match those applied in practice at large-scale deployments, and design time- and data-efficient algorithms for these settings. Finally, we will experiment with and tune theoretical algorithms to make code which is effective on real data. While there has been significant work conducted on privacy and statistics, this work differs primarily in two ways: a focus on understanding properties of the underlying population, rather than a specific data set, and investigating the cost of privacy with finite amounts of data, rather than the "asymptotic" setting where the amount of data tends to infinity. As statistical methods are only becoming more and more common, and privacy concerns are an increasingly common topic of public discourse, the importance of rigorous methods for private statistics is paramount. In particular, due to recent events demonstrating the power of massive amounts of user data (e.g., the Facebook-Cambridge Analytica data scandal), significant amounts of new policy are likely to be written to prevent such events from reoccurring. In turn, this will necessitate new highly qualified personnel trained in data privacy at virtually every company which deals with user data -- roles which my students will be prepared to fill.