Statistical Inference in the Differential Privacy Model

Abstract

In modern settings of data analysis, we may be running our algorithms on datasets that are sensitive in nature. However, classical machine learning and statistical algorithms were not designed with these risks in mind, and it has been demonstrated that they may reveal personal information. These concerns disincentivize individuals from providing their data, or even worse, encouraging intentionally providing fake data. To assuage these concerns, we import the constraint of differential privacy to the statistical inference, considered by many to be the gold standard of data privacy. This thesis aims to quantify the cost of ensuring differential privacy, i.e., understanding how much additional data is required to perform data analysis with the constraint of differential privacy. Despite the maturity of the literature on differential privacy, there is still inadequate understanding in some of the most fundamental settings. In particular, we make progress in the following problems: $\bullet$ What is the sample complexity of DP hypothesis testing? $\bullet$ Can we privately estimate distribution properties with a negligible cost? $\bullet$ What is the fundamental limit in private distribution estimation? $\bullet$ How can we design algorithms to privately estimate random graphs? $\bullet$ What is the trade-off between the sample complexity and the interactivity in private hypothesis selection?

This thesis is a summary of the author's several works during his Ph.D. Besides, it has established the optimal sample complexity of differentially private closeness testing

References in corpus (11)

• Differential Privacy as a Mutual Information Constraint
• Privacy and Statistical Risk: Formalisms and Minimax Bounds
• Improved Information Gain Estimates for Decision Tree Induction
• Graphical-model based estimation and inference for differential privacy
• Communication Complexity in Locally Private Distribution Estimation and Heavy Hitters
• Information Theoretic Properties of Markov Random Fields, and their Algorithmic Applications
• New Oracle-Efficient Algorithms for Private Synthetic Data Release
• A Primer on Private Statistics
• Density estimation in linear time
• Structure learning of antiferromagnetic Ising models
• Robust Testing and Estimation under Manipulation Attacks