We study the minimax cost of $(\varepsilon,δ)$-differential privacy for mean estimation and Gaussian linear regression in low and high dimensions. For low-dimensional mean estimation, a resampling reduction to fingerprinting yields the privacy contribution $d^2\log(1/δ)/(n^2\varepsilon^2)$ in the stated polynomial-$δ$ regime. For low-dimensional regression, a tracing argument gives the contribution $d^2/(n^2\varepsilon^2)$ under an explicit approximate-DP remainder condition. For sparse mean estimation and sparse regression, a constant-weight packing and a private Fano lemma produce an effective privacy entropy of order $\min\{s\log(ed/s),[\log((e^\varepsilon-1)/δ)]_+\}$ for $δ>0$, up to universal constants and a fixed threshold; for pure DP it is $s\log(ed/s)$. Thus, when $δ$ is polynomially smaller than $\varepsilon$, the pure-DP dependence is retained up to polylogarithmic factors whenever the effective dimension is polylogarithmic in $n$, including regimes with $\varepsilon=o(1)$. Coordinatewise-clipping estimators for means and split-sample noisy-gradient estimators for regression attain the lower bounds up to explicit logarithmic factors. Simulations and data examples illustrate related implementations.
This chapter is meant to be part of the book "Differential Privacy for Artificial Intelligence Applications." We give an introduction to the most important property of differential privacy -- composition: running multiple independent analyses on the data of a set of people will still be differentially private as long as each of the analyses is private on its own -- as well as the related topic of privacy amplification by subsampling. This chapter introduces the basic concepts and gives proofs of the key results needed to apply these tools in practice.
Differential privacy is often applied with a privacy parameter that is larger than the theory suggests is ideal; various informal justifications for tolerating large privacy parameters have been proposed. In this work, we consider partial differential privacy (DP), which allows quantifying the privacy guarantee on a per-attribute basis. In this framework, we study several basic data analysis and learning tasks, and design algorithms whose per-attribute privacy parameter is smaller that the best possible privacy parameter for the entire record of a person (i.e., all the attributes).
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…
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…
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 …
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…
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…
"Concentrated differential privacy" was recently introduced by Dwork and Rothblum as a relaxation of differential privacy, which permits sharper analyses of many privacy-preserving computations. We present an alternative formulation of the concept of concentrated differential privacy in terms of the Renyi divergence between the distributions obtained by running an algorithm on neighboring inputs. With this reformulation in hand, we prove sharper quantitative results, establish lower bounds, and raise a few new questions. We also unify this approach with approximate differential privacy by givi…
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…
University of Kalyani（卡利亚尼大学）；National Institute of Science, Education and Research Bhubaneswar（布巴内斯瓦尔国家科学教育与研究学院）；Homi Bhaba National Institute（霍米·巴巴国家学院）
The leakage of data might have been an extreme effect on the personal level if it contains sensitive information. Common prevention methods like encryption-decryption, endpoint protection, intrusion detection system are prone to leakage. Differential privacy comes to the rescue with a proper promise of protection against leakage, as it uses a randomized response technique at the time of collection of the data which promises strong privacy with better utility. Differential privacy allows one to access the forest of data by describing their pattern of groups without disclosing any individual tre…
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, …
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…
Attacks that aim to identify the training data of public neural networks represent a severe threat to the privacy of individuals participating in the training data set. A possible protection is offered by anonymization of the training data or training function with differential privacy. However, data scientists can choose between local and central differential privacy and need to select meaningful privacy parameters $ε$ which is challenging for non-privacy experts. We empirically compare local and central differential privacy mechanisms under white- and black-box membership inference to evalua…
We show how to achieve differential privacy with no or reduced added noise, based on the empirical noise in the data itself. Unlike previous works on noiseless privacy, the empirical viewpoint avoids making any explicit assumptions about the random process generating the data.
Since its conception in 2006, differential privacy has emerged as the de-facto standard in data privacy, owing to its robust mathematical guarantees, generalised applicability and rich body of literature. Over the years, researchers have studied differential privacy and its applicability to an ever-widening field of topics. Mechanisms have been created to optimise the process of achieving differential privacy, for various data types and scenarios. Until this work however, all previous work on differential privacy has been conducted on a ad-hoc basis, without a single, unifying codebase to impl…
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…
We propose a relaxed privacy definition called {\em random differential privacy} (RDP). Differential privacy requires that adding any new observation to a database will have small effect on the output of the data-release procedure. Random differential privacy requires that adding a {\em randomly drawn new observation} to a database will have small effect on the output. We show an analog of the composition property of differentially private procedures which applies to our new definition. We show how to release an RDP histogram and we show that RDP histograms are much more accurate than histogra…
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 …
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…
Bayesian learning via Stochastic Gradient Langevin Dynamics (SGLD) has been suggested for differentially private learning. While previous research provides differential privacy bounds for SGLD at the initial steps of the algorithm or when close to convergence, the question of what differential privacy guarantees can be made in between remains unanswered. This interim region is of great importance, especially for Bayesian neural networks, as it is hard to guarantee convergence to the posterior. This paper shows that using SGLD might result in unbounded privacy loss for this interim region, even…
While differential privacy and gradient compression are separately well-researched topics in machine learning, the study of interaction between these two topics is still relatively new. We perform a detailed empirical study on how the Gaussian mechanism for differential privacy and gradient compression jointly impact test accuracy in deep learning. The existing literature in gradient compression mostly evaluates compression in the absence of differential privacy guarantees, and demonstrate that sufficiently high compression rates reduce accuracy. Similarly, existing literature in differential …
We show that Gaussian Differential Privacy, a variant of differential privacy tailored to the analysis of Gaussian noise addition, composes gracefully even in the presence of a fully adaptive analyst. Such an analyst selects mechanisms (to be run on a sensitive data set) and their privacy budgets adaptively, that is, based on the answers from other mechanisms run previously on the same data set. In the language of Rogers, Roth, Ullman and Vadhan, this gives a filter for GDP with the same parameters as for nonadaptive composition.
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.
University of Marburg（马尔堡大学）；University of Copenhagen（哥本哈根大学）；Topdanmark A/S（Topdanmark公司）；Manipal Institute of Technology（马尼帕尔理工学院）
The performance cost of differential privacy has, for some applications, been shown to be higher for minority groups; fairness, conversely, has been shown to disproportionally compromise the privacy of members of such groups. Most work in this area has been restricted to computer vision and risk assessment. In this paper, we evaluate the impact of differential privacy on fairness across four tasks, focusing on how attempts to mitigate privacy violations and between-group performance differences interact: Does privacy inhibit attempts to ensure fairness? To this end, we train $(\varepsilon,δ)$-…
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…
Microsoft（微软）；University of Pennsylvania（宾夕法尼亚大学）；Stanford University（斯坦福大学）
We show that adding differential privacy to Explainable Boosting Machines (EBMs), a recent method for training interpretable ML models, yields state-of-the-art accuracy while protecting privacy. Our experiments on multiple classification and regression datasets show that DP-EBM models suffer surprisingly little accuracy loss even with strong differential privacy guarantees. In addition to high accuracy, two other benefits of applying DP to EBMs are: a) trained models provide exact global and local interpretability, which is often important in settings where differential privacy is needed; and …
Duke University（杜克大学）；University at Buffalo, SUNY（纽约州立大学布法罗分校）；Nanjing University（南京大学）
Significant success has been realized recently on applying machine learning to real-world applications. There have also been corresponding concerns on the privacy of training data, which relates to data security and confidentiality issues. Differential privacy provides a principled and rigorous privacy guarantee on machine learning models. While it is common to design a model satisfying a required differential-privacy property by injecting noise, it is generally hard to balance the trade-off between privacy and utility. We show that stochastic gradient Markov chain Monte Carlo (SG-MCMC) -- a c…
Technical University of Munich（慕尼黑工业大学）；Ludwig Maximilian University of Munich（慕尼黑大学）；Imperial College London（帝国理工学院）；Helmholtz Zentrum Munich（慕尼黑亥姆霍兹中心）
Differential privacy (DP) is typically formulated as a worst-case privacy guarantee over all individuals in a database. More recently, extensions to individual subjects or their attributes, have been introduced. Under the individual/per-instance DP interpretation, we study the connection between the per-subject gradient norm in DP neural networks and individual privacy loss and introduce a novel metric termed the Privacy Loss-Input Susceptibility (PLIS), which allows one to apportion the subject's privacy loss to their input attributes. We experimentally show how this enables the identificatio…
Google AI（谷歌人工智能（Google AI））；New York, NY 10011（纽约州纽约市（邮编10011））
We characterize the minimum noise amplitude and power for noise-adding mechanisms in $(ε, δ)$-differential privacy for single real-valued query function. We derive new lower bounds using the duality of linear programming, and new upper bounds by proposing a new class of $(ε,δ)$-differentially private mechanisms, the \emph{truncated Laplacian} mechanisms. We show that the multiplicative gap of the lower bounds and upper bounds goes to zero in various high privacy regimes, proving the tightness of the lower and upper bounds and thus establishing the optimality of the truncated Laplacian mechanis…
Differential Privacy can provide provable privacy guarantees for training data in machine learning. However, the presence of proofs does not preclude the presence of errors. Inspired by recent advances in auditing which have been used for estimating lower bounds on differentially private algorithms, here we show that auditing can also be used to find flaws in (purportedly) differentially private schemes. In this case study, we audit a recent open source implementation of a differentially private deep learning algorithm and find, with 99.99999999% confidence, that the implementation does not sa…
Differential privacy is a framework for privately releasing summaries of a database. Previous work has focused mainly on methods for which the output is a finite dimensional vector, or an element of some discrete set. We develop methods for releasing functions while preserving differential privacy. Specifically, we show that adding an appropriate Gaussian process to the function of interest yields differential privacy. When the functions lie in the same RKHS as the Gaussian process, then the correct noise level is established by measuring the "sensitivity" of the function in the RKHS norm. As …
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…
University of Southern California（南加州大学）；Tsinghua University（清华大学）；Indiana University（印第安纳大学）
In June 2016, Apple announced that it will deploy differential privacy for some user data collection in order to ensure privacy of user data, even from Apple. The details of Apple's approach remained sparse. Although several patents have since appeared hinting at the algorithms that may be used to achieve differential privacy, they did not include a precise explanation of the approach taken to privacy parameter choice. Such choice and the overall approach to privacy budget use and management are key questions for understanding the privacy protections provided by any deployment of differential …
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；University of Oxford（牛津大学）
When learning from sensitive data, care must be taken to ensure that training algorithms address privacy concerns. The canonical Private Aggregation of Teacher Ensembles, or PATE, computes output labels by aggregating the predictions of a (possibly distributed) collection of teacher models via a voting mechanism. The mechanism adds noise to attain a differential privacy guarantee with respect to the teachers' training data. In this work, we observe that this use of noise, which makes PATE predictions stochastic, enables new forms of leakage of sensitive information. For a given input, our adve…
Tsinghua University（清华大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Smart meter devices enable a better understanding of the demand at the potential risk of private information leakage. One promising solution to mitigating such risk is to inject noises into the meter data to achieve a certain level of differential privacy. In this paper, we cast one-shot non-intrusive load monitoring (NILM) in the compressive sensing framework, and bridge the gap between theoretical accuracy of NILM inference and differential privacy's parameters. We then derive the valid theoretical bounds to offer insights on how the differential privacy parameters affect the NILM performanc…
Nowadays, owners and developers of deep learning models must consider stringent privacy-preservation rules of their training data, usually crowd-sourced and retaining sensitive information. The most widely adopted method to enforce privacy guarantees of a deep learning model nowadays relies on optimization techniques enforcing differential privacy. According to the literature, this approach has proven to be a successful defence against several models' privacy attacks, but its downside is a substantial degradation of the models' performance. In this work, we compare the effectiveness of the dif…
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…
International Institute of Information Technology (IIIT), Hyderabad（国际信息技术学院（海得拉巴））
Deep learning's unprecedented success raises several ethical concerns ranging from biased predictions to data privacy. Researchers tackle these issues by introducing fairness metrics, or federated learning, or differential privacy. A first, this work presents an ethical federated learning model, incorporating all three measures simultaneously. Experiments on the Adult, Bank and Dutch datasets highlight the resulting ``empirical interplay" between accuracy, fairness, and privacy.
The objective of machine learning is to extract useful information from data, while privacy is preserved by concealing information. Thus it seems hard to reconcile these competing interests. However, they frequently must be balanced when mining sensitive data. For example, medical research represents an important application where it is necessary both to extract useful information and protect patient privacy. One way to resolve the conflict is to extract general characteristics of whole populations without disclosing the private information of individuals. In this paper, we consider differenti…
One barrier to more widespread adoption of differentially private neural networks is the entailed accuracy loss. To address this issue, the relationship between neural network architectures and model accuracy under differential privacy constraints needs to be better understood. As a first step, we test whether extant knowledge on architecture design also holds in the differentially private setting. Our findings show that it does not; architectures that perform well without differential privacy, do not necessarily do so with differential privacy. Consequently, extant knowledge on neural network…
Differential Privacy (DP) is a formal definition of privacy that provides rigorous guarantees against risks of privacy breaches during data processing. It makes no assumptions about the knowledge or computational power of adversaries, and provides an interpretable, quantifiable and composable formalism. DP has been actively researched during the last 15 years, but it is still hard to master for many Machine Learning (ML)) practitioners. This paper aims to provide an overview of the most important ideas, concepts and uses of DP in ML, with special focus on its intersection with Federated Learni…
Nowadays, the development of information technology is growing rapidly. In the big data era, the privacy of personal information has been more pronounced. The major challenge is to find a way to guarantee that sensitive personal information is not disclosed while data is published and analyzed. Centralized differential privacy is established on the assumption of a trusted third-party data curator. However, this assumption is not always true in reality. As a new privacy preservation model, local differential privacy has relatively strong privacy guarantees. Although federated learning has relat…
