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Register a new userStatistical Inference in the Differential Privacy Model
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Added by
Huanyu Zhang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Authors
Huanyu Zhang
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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?
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We study privacy in a distributed learning framework, where clients collaboratively build a learning model iteratively through interactions with a server from whom we need privacy. Motivated by stochastic optimization and the federated learning (FL) paradigm, we focus on the case where a small fraction of data samples are randomly sub-sampled in each round to participate in the learning process, which also enables privacy amplification. To obtain even stronger local privacy guarantees, we study this in the shuffle privacy model, where each client randomizes its response using a local differentially private (LDP) mechanism and the server only receives a random permutation (shuffle) of the clients responses without their association to each client. The principal result of this paper is a privacy-optimization performance trade-off for discrete randomization mechanisms in this sub-sampled shuffle privacy model. This is enabled through a new theoretical technique to analyze the Renyi Differential Privacy (RDP) of the sub-sampled shuffle model. We numerically demonstrate that, for important regimes, with composition our bound yields significant improvement in privacy guarantee over the state-of-the-art approximate Differential Privacy (DP) guarantee (with strong composition) for sub-sampled shuffled models. We also demonstrate numerically significant improvement in privacy-learning performance operating point using real data sets.
Many privacy mechanisms reveal high-level information about a data distribution through noisy measurements. It is common to use this information to estimate the answers to new queries. In this work, we provide an approach to solve this estimation problem efficiently using graphical models, which is particularly effective when the distribution is high-dimensional but the measurements are over low-dimensional marginals. We show that our approach is far more efficient than existing estimation techniques from the privacy literature and that it can improve the accuracy and scalability of many state-of-the-art mechanisms.
We give a fast algorithm to optimally compose privacy guarantees of differentially private (DP) algorithms to arbitrary accuracy. Our method is based on the notion of privacy loss random variables to quantify the privacy loss of DP algorithms. The running time and memory needed for our algorithm to approximate the privacy curve of a DP algorithm composed with itself $k$ times is $tilde{O}(sqrt{k})$. This improves over the best prior method by Koskela et al. (2020) which requires $tilde{Omega}(k^{1.5})$ running time. We demonstrate the utility of our algorithm by accurately computing the privacy loss of DP-SGD algorithm of Abadi et al. (2016) and showing that our algorithm speeds up the privacy computations by a few orders of magnitude compared to prior work, while maintaining similar accuracy.
We study how to communicate findings of Bayesian inference to third parties, while preserving the strong guarantee of differential privacy. Our main contributions are four different algorithms for private Bayesian inference on proba-bilistic graphical models. These include two mechanisms for adding noise to the Bayesian updates, either directly to the posterior parameters, or to their Fourier transform so as to preserve update consistency. We also utilise a recently introduced posterior sampling mechanism, for which we prove bounds for the specific but general case of discrete Bayesian networks; and we introduce a maximum-a-posteriori private mechanism. Our analysis includes utility and privacy bounds, with a novel focus on the influence of graph structure on privacy. Worked examples and experiments with Bayesian na{i}ve Bayes and Bayesian linear regression illustrate the application of our mechanisms.
LDP (Local Differential Privacy) has been widely studied to estimate statistics of personal data (e.g., distribution underlying the data) while protecting users privacy. Although LDP does not require a trusted third party, it regards all personal data equally sensitive, which causes excessive obfuscation hence the loss of utility. In this paper, we introduce the notion of ULDP (Utility-optimized LDP), which provides a privacy guarantee equivalent to LDP only for sensitive data. We first consider the setting where all users use the same obfuscation mechanism, and propose two mechanisms providing ULDP: utility-optimized randomized response and utility-optimized RAPPOR. We then consider the setting where the distinction between sensitive and non-sensitive data can be different from user to user. For this setting, we propose a personalized ULDP mechanism with semantic tags to estimate the distribution of personal data with high utility while keeping secret what is sensitive for each user. We show theoretically and experimentally that our mechanisms provide much higher utility than the existing LDP mechanisms when there are a lot of non-sensitive data. We also show that when most of the data are non-sensitive, our mechanisms even provide almost the same utility as non-private mechanisms in the low privacy regime.
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