In this paper we study the problem of estimating the unknown mean $θ$ of a unit variance Gaussian distribution in a locally differentially private (LDP) way. In the high-privacy regime ($ε\le 1$), we identify an optimal privacy mechanism that minimizes the variance of the estimator asymptotically. Our main technical contribution is the maximization of the Fisher-Information of the sanitized data with respect to the local privacy mechanism $Q$. We find that the exact solution $Q_{θ,ε}$ of this maximization is the sign mechanism that applies randomized response to the sign of $X_i-θ$, where $X_1,\dots, X_n$ are the confidential iid original samples. However, since this optimal local mechanism depends on the unknown mean $θ$, we employ a two-stage LDP parameter estimation procedure which requires splitting agents into two groups. The first $n_1$ observations are used to consistently but not necessarily efficiently estimate the parameter $θ$ by $\tildeθ_{n_1}$. Then this estimate is updated by applying the sign mechanism with $\tildeθ_{n_1}$ instead of $θ$ to the remaining $n-n_1$ observations, to obtain an LDP and efficient estimator of the unknown mean.
In the recent years, Local Differential Privacy (LDP) has been one of the corner stone of privacy preserving data analysis. However, many challenges still opposes its widespread application. One of these problems is the scalability of LDP to high dimensional data, in particular for estimating joint-distributions. In this paper, we develop an approximate estimator for frequency joint-distribution estimation under so-called pure LDP protocols.
In this rejoinder, we aim to address two broad issues that cover most comments made in the discussion. First, we discuss some theoretical aspects of our work and comment on how this work might impact the theoretical foundation of privacy-preserving data analysis. Taking a practical viewpoint, we next discuss how f-differential privacy (f-DP) and Gaussian differential privacy (GDP) can make a difference in a range of applications.
We consider the binary classification problem in a setup that preserves the privacy of the original sample. We provide a privacy mechanism that is locally differentially private and then construct a classifier based on the private sample that is universally consistent in Euclidean spaces. Under stronger assumptions, we establish the minimax rates of convergence of the excess risk and see that they are slower than in the case when the original sample is available.
In this work, we introduce a new approach for statistical quantification of differential privacy in a black box setting. We present estimators and confidence intervals for the optimal privacy parameter of a randomized algorithm $A$, as well as other key variables (such as the "data-centric privacy level"). Our estimators are based on a local characterization of privacy and in contrast to the related literature avoid the process of "event selection" - a major obstacle to privacy validation. This makes our methods easy to implement and user-friendly. We show fast convergence rates of the estimat…
Differential Privacy (DP) is the leading approach to privacy preserving deep learning. As such, there are multiple efforts to provide drop-in integration of DP into popular frameworks. These efforts, which add noise to each gradient computation to make it DP, rely on composition theorems to bound the total privacy loss incurred over this sequence of DP computations. However, existing composition theorems present a tension between efficiency and flexibility. Most theorems require all computations in the sequence to have a predefined DP parameter, called the privacy budget. This prevents the des…
The Sampled Gaussian Mechanism (SGM)---a composition of subsampling and the additive Gaussian noise---has been successfully used in a number of machine learning applications. The mechanism's unexpected power is derived from privacy amplification by sampling where the privacy cost of a single evaluation diminishes quadratically, rather than linearly, with the sampling rate. Characterizing the precise privacy properties of SGM motivated development of several relaxations of the notion of differential privacy. This work unifies and fills in gaps in published results on SGM. We describe a numerica…
Federated learning (FL) is a training paradigm where the clients collaboratively learn models by repeatedly sharing information without compromising much on the privacy of their local sensitive data. In this paper, we introduce federated $f$-differential privacy, a new notion specifically tailored to the federated setting, based on the framework of Gaussian differential privacy. Federated $f$-differential privacy operates on record level: it provides the privacy guarantee on each individual record of one client's data against adversaries. We then propose a generic private federated learning fr…
China University of Geosciences（中国地质大学）；University of Technology, Sydney（悉尼科技大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Artificial Intelligence (AI) has attracted a great deal of attention in recent years. However, alongside all its advancements, problems have also emerged, such as privacy violations, security issues and model fairness. Differential privacy, as a promising mathematical model, has several attractive properties that can help solve these problems, making it quite a valuable tool. For this reason, differential privacy has been broadly applied in AI but to date, no study has documented which differential privacy mechanisms can or have been leveraged to overcome its issues or the properties that make…
We consider the problem of reinforcing federated learning with formal privacy guarantees. We propose to employ Bayesian differential privacy, a relaxation of differential privacy for similarly distributed data, to provide sharper privacy loss bounds. We adapt the Bayesian privacy accounting method to the federated setting and suggest multiple improvements for more efficient privacy budgeting at different levels. Our experiments show significant advantage over the state-of-the-art differential privacy bounds for federated learning on image classification tasks, including a medical application, …
Northwest University（西北大学）；Macau University of Science and Technology（澳门科技大学）
In this paper, we present a differential privacy version of convex and nonconvex sparse classification approach. Based on alternating direction method of multiplier (ADMM) algorithm, we transform the solving of sparse problem into the multistep iteration process. Then we add exponential noise to stable steps to achieve privacy protection. By the property of the post-processing holding of differential privacy, the proposed approach satisfies the $ε-$differential privacy even when the original problem is unstable. Furthermore, we present the theoretical privacy bound of the differential privacy …
Communication and privacy are two critical concerns in distributed learning. Many existing works treat these concerns separately. In this work, we argue that a natural connection exists between methods for communication reduction and privacy preservation in the context of distributed machine learning. In particular, we prove that Count Sketch, a simple method for data stream summarization, has inherent differential privacy properties. Using these derived privacy guarantees, we propose a novel sketch-based framework (DiffSketch) for distributed learning, where we compress the transmitted messag…
Differential Privacy (DP) provides strong guarantees on the risk of compromising a user's data in statistical learning applications, though these strong protections make learning challenging and may be too stringent for some use cases. To address this, we propose element level differential privacy, which extends differential privacy to provide protection against leaking information about any particular "element" a user has, allowing better utility and more robust results than classical DP. By carefully choosing these "elements," it is possible to provide privacy protections at a desired granul…
The purpose of this paper is to guide interpretation of the semantic privacy guarantees for some of the major variations of differential privacy, which include pure, approximate, Rényi, zero-concentrated, and $f$ differential privacy. We interpret privacy-loss accounting parameters, frequentist semantics, and Bayesian semantics (including new results). The driving application is the interpretation of the confidentiality protections for the 2020 Census Public Law 94-171 Redistricting Data Summary File released August 12, 2021, which, for the first time, were produced with formal privacy guarant…
Black-box machine learning models are used in critical decision-making domains, giving rise to several calls for more algorithmic transparency. The drawback is that model explanations can leak information about the training data and the explanation data used to generate them, thus undermining data privacy. To address this issue, we propose differentially private algorithms to construct feature-based model explanations. We design an adaptive differentially private gradient descent algorithm, that finds the minimal privacy budget required to produce accurate explanations. It reduces the overall …
Differential privacy, a notion of algorithmic stability, is a gold standard for measuring the additional risk an algorithm's output poses to the privacy of a single record in the dataset. Differential privacy is defined as the distance between the output distribution of an algorithm on neighboring datasets that differ in one entry. In this work, we present a novel relaxation of differential privacy, capacity bounded differential privacy, where the adversary that distinguishes output distributions is assumed to be capacity-bounded -- i.e. bounded not in computational power, but in terms of the …
University of Amsterdam（阿姆斯特丹大学）；VU Amsterdam（阿姆斯特丹自由大学）
Differentially private learning on real-world data poses challenges for standard machine learning practice: privacy guarantees are difficult to interpret, hyperparameter tuning on private data reduces the privacy budget, and ad-hoc privacy attacks are often required to test model privacy. We introduce three tools to make differentially private machine learning more practical: (1) simple sanity checks which can be carried out in a centralized manner before training, (2) an adaptive clipping bound to reduce the effective number of tuneable privacy parameters, and (3) we show that large-batch tra…
Artificial Intelligence Lab, Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院人工智能实验室）
Traditional differential privacy is independent of the data distribution. However, this is not well-matched with the modern machine learning context, where models are trained on specific data. As a result, achieving meaningful privacy guarantees in ML often excessively reduces accuracy. We propose Bayesian differential privacy (BDP), which takes into account the data distribution to provide more practical privacy guarantees. We also derive a general privacy accounting method under BDP, building upon the well-known moments accountant. Our experiments demonstrate that in-distribution samples in …
Deep learning models are often trained on datasets that contain sensitive information such as individuals' shopping transactions, personal contacts, and medical records. An increasingly important line of work therefore has sought to train neural networks subject to privacy constraints that are specified by differential privacy or its divergence-based relaxations. These privacy definitions, however, have weaknesses in handling certain important primitives (composition and subsampling), thereby giving loose or complicated privacy analyses of training neural networks. In this paper, we consider a…
Carlson School of Management, University of Minnesota（明尼苏达大学卡尔森管理学院）；School of Statistics, University of Minnesota（明尼苏达大学统计学院）
Differential privacy is becoming one gold standard for protecting the privacy of publicly shared data. It has been widely used in social science, data science, public health, information technology, and the U.S. decennial census. Nevertheless, to guarantee differential privacy, existing methods may unavoidably alter the conclusion of the original data analysis, as privatization often changes the sample distribution. This phenomenon is known as the trade-off between privacy protection and statistical accuracy. In this work, we mitigate this trade-off by developing a distribution-invariant priva…
University of Tübingen（蒂宾根大学）；University of Siegen（锡根大学）
New generation head-mounted displays, such as VR and AR glasses, are coming into the market with already integrated eye tracking and are expected to enable novel ways of human-computer interaction in numerous applications. However, since eye movement properties contain biometric information, privacy concerns have to be handled properly. Privacy-preservation techniques such as differential privacy mechanisms have recently been applied to eye movement data obtained from such displays. Standard differential privacy mechanisms; however, are vulnerable due to temporal correlations between the eye m…
We study the problem of subsampling in differential privacy (DP), a question that is the centerpiece behind many successful differentially private machine learning algorithms. Specifically, we provide a tight upper bound on the Rényi Differential Privacy (RDP) (Mironov, 2017) parameters for algorithms that: (1) subsample the dataset, and then (2) applies a randomized mechanism M to the subsample, in terms of the RDP parameters of M and the subsampling probability parameter. Our results generalize the moments accounting technique, developed by Abadi et al. (2016) for the Gaussian mechanism, to …
Differential privacy is a useful tool to build machine learning models which do not release too much information about the training data. We study the Rényi differential privacy of stochastic gradient descent when each training example is sampled without replacement (also known as cyclic SGD). Cyclic SGD is typically faster than traditional SGD and is the algorithm of choice in large-scale implementations. We recover privacy guarantees for cyclic SGD which are competitive with those known for sampling with replacement. Our proof techniques make no assumptions on the model or on the data and ar…
Andalusian Research Institute in Data Science and Computational Intelligence, University of Granada（格拉纳达大学安达卢西亚数据科学与计算智能研究所）
The high demand of artificial intelligence services at the edges that also preserve data privacy has pushed the research on novel machine learning paradigms that fit those requirements. Federated learning has the ambition to protect data privacy through distributed learning methods that keep the data in their data silos. Likewise, differential privacy attains to improve the protection of data privacy by measuring the privacy loss in the communication among the elements of federated learning. The prospective matching of federated learning and differential privacy to the challenges of data priva…
