Quantiles are often used for summarizing and understanding data. If that data is sensitive, it may be necessary to compute quantiles in a way that is differentially private, providing theoretical guarantees that the result does not reveal private information. However, when multiple quantiles are needed, existing differentially private algorithms fare poorly: they either compute quantiles individually, splitting the privacy budget, or summarize the entire distribution, wasting effort. In either case the result is reduced accuracy. In this work we propose an instance of the exponential mechanism that simultaneously estimates exactly $m$ quantiles from $n$ data points while guaranteeing differential privacy. The utility function is carefully structured to allow for an efficient implementation that returns estimates of all $m$ quantiles in time $O(mn\log(n) + m^2n)$. Experiments show that our method significantly outperforms the current state of the art on both real and synthetic data while remaining efficient enough to be practical.
Tel Aviv University（特拉维夫大学）；Google Research（谷歌研究院）；Ben-Gurion University（本古里安大学）；Ben-Gurion University of the Negev（内盖夫本古里安大学）
In this work we study the problem of differentially private (DP) quantiles, in which given dataset $X$ and quantiles $q_1, ..., q_m \in [0,1]$, we want to output $m$ quantile estimations which are as close as possible to the true quantiles and preserve DP. We describe a simple recursive DP algorithm, which we call ApproximateQuantiles (AQ), for this task. We give a worst case upper bound on its error, and show that its error is much lower than of previous implementations on several different datasets. Furthermore, it gets this low error while running time two orders of magnitude faster that th…
Khoury College of Computer Sciences, Northeastern University（东北大学胡里计算机科学学院）
We investigate whether Differentially Private SGD offers better privacy in practice than what is guaranteed by its state-of-the-art analysis. We do so via novel data poisoning attacks, which we show correspond to realistic privacy attacks. While previous work (Ma et al., arXiv 2019) proposed this connection between differential privacy and data poisoning as a defense against data poisoning, our use as a tool for understanding the privacy of a specific mechanism is new. More generally, our work takes a quantitative, empirical approach to understanding the privacy afforded by specific implementa…
We develop a new reduction that converts any online convex optimization algorithm suffering $O(\sqrt{T})$ regret into an $ε$-differentially private stochastic convex optimization algorithm with the optimal convergence rate $\tilde O(1/\sqrt{T} + \sqrt{d}/εT)$ on smooth losses in linear time, forming a direct analogy to the classical non-private "online-to-batch" conversion. By applying our techniques to more advanced adaptive online algorithms, we produce adaptive differentially private counterparts whose convergence rates depend on apriori unknown variances or parameter norms.
This paper presents a differentially private algorithm for linear regression learning in a decentralized fashion. Under this algorithm, privacy budget is theoretically derived, in addition to that the solution error is shown to be bounded by $O(t)$ for $O(1/t)$ descent step size and $O(\exp(t^{1-e}))$ for $O(t^{-e})$ descent step size.
Differentially private models seek to protect the privacy of data the model is trained on, making it an important component of model security and privacy. At the same time, data scientists and machine learning engineers seek to use uncertainty quantification methods to ensure models are as useful and actionable as possible. We explore the tension between uncertainty quantification via dropout and privacy by conducting membership inference attacks against models with and without differential privacy. We find that models with large dropout slightly increases a model's risk to succumbing to membe…
Clustering is an essential primitive in unsupervised machine learning. We bring forth the problem of sublinear-time differentially-private clustering as a natural and well-motivated direction of research. We combine the $k$-means and $k$-median sublinear-time results of Mishra et al. (SODA, 2001) and of Czumaj and Sohler (Rand. Struct. and Algorithms, 2007) with recent results on private clustering of Balcan et al. (ICML 2017), Gupta et al. (SODA, 2010) and Ghazi et al. (NeurIPS, 2020) to obtain sublinear-time private $k$-means and $k$-median algorithms via subsampling. We also investigate the…
Department of Computer Science, Georgetown University（乔治城大学计算机科学系）
We present the first nearly optimal differentially private PAC learner for any concept class with VC dimension 1 and Littlestone dimension $d$. Our algorithm achieves the sample complexity of $\tilde{O}_{\varepsilon,δ,α,δ}(\log^* d)$, nearly matching the lower bound of $Ω(\log^* d)$ proved by Alon et al. [STOC19]. Prior to our work, the best known upper bound is $\tilde{O}(VC\cdot d^5)$ for general VC classes, as shown by Ghazi et al. [STOC21].
The application of differential privacy to the training of deep neural networks holds the promise of allowing large-scale (decentralized) use of sensitive data while providing rigorous privacy guarantees to the individual. The predominant approach to differentially private training of neural networks is DP-SGD, which relies on norm-based gradient clipping as a method for bounding sensitivity, followed by the addition of appropriately calibrated Gaussian noise. In this work we propose NeuralDP, a technique for privatising activations of some layer within a neural network, which by the post-proc…
College of Information and Computer Sciences（信息与计算机科学学院）；University of Massachusetts（马萨诸塞大学）
Many differentially private algorithms for answering database queries involve a step that reconstructs a discrete data distribution from noisy measurements. This provides consistent query answers and reduces error, but often requires space that grows exponentially with dimension. Private-PGM is a recent approach that uses graphical models to represent the data distribution, with complexity proportional to that of exact marginal inference in a graphical model with structure determined by the co-occurrence of variables in the noisy measurements. Private-PGM is highly scalable for sparse measurem…
University of California San Diego（加州大学圣迭戈分校）；Microsoft Research（微软研究院）；Microsoft（微软）
Recent papers have shown that large pre-trained language models (LLMs) such as BERT, GPT-2 can be fine-tuned on private data to achieve performance comparable to non-private models for many downstream Natural Language Processing (NLP) tasks while simultaneously guaranteeing differential privacy. The inference cost of these models -- which consist of hundreds of millions of parameters -- however, can be prohibitively large. Hence, often in practice, LLMs are compressed before they are deployed in specific applications. In this paper, we initiate the study of differentially private model compres…
Linear $L_1$-regularized models have remained one of the simplest and most effective tools in data analysis, especially in information retrieval problems where n-grams over text with TF-IDF or Okapi feature values are a strong and easy baseline. Over the past decade, screening rules have risen in popularity as a way to reduce the runtime for producing the sparse regression weights of $L_1$ models. However, despite the increasing need of privacy-preserving models in information retrieval, to the best of our knoweledge, no differentially private screening rule exists. In this paper, we develop t…
Data poisoning attacks aim to manipulate the model produced by a learning algorithm by adversarially modifying the training set. We consider differential privacy as a defensive measure against this type of attack. We show that such learners are resistant to data poisoning attacks when the adversary is only able to poison a small number of items. However, this protection degrades as the adversary poisons more data. To illustrate, we design attack algorithms targeting objective and output perturbation learners, two standard approaches to differentially-private machine learning. Experiments show …
the University of Adelaide（阿德莱德大学）；Sun Yat-sen University（中山大学）
Iterative clustering algorithms help us to learn the insights behind the data. Unfortunately, this may allow adversaries to infer the privacy of individuals with some background knowledge. In the worst case, the adversaries know the centroids of an arbitrary iteration and the information of n-1 out of n items. To protect individual privacy against such an inference attack, preserving differential privacy (DP) for the iterative clustering algorithms has been extensively studied in the interactive settings. However, existing interactive differentially private clustering algorithms suffer from a …
Technical University of Munich（慕尼黑工业大学）；Imperial College London（伦敦帝国学院）
The training of neural networks with Differentially Private Stochastic Gradient Descent offers formal Differential Privacy guarantees but introduces accuracy trade-offs. In this work, we propose to alleviate these trade-offs in residual networks with Group Normalisation through a simple architectural modification termed ScaleNorm by which an additional normalisation layer is introduced after the residual block's addition operation. Our method allows us to further improve on the recently reported state-of-the art on CIFAR-10, achieving a top-1 accuracy of 82.5% (ε=8.0) when trained from scratch…
We introduce a new algorithm, Construction of dIfferentially Private Empirical Distributions from a low-order marginals set tHrough solving linear Equations with l2 Regularization (CIPHER), that produces differentially private empirical joint distributions from a set of low-order marginals. CIPHER is conceptually simple and requires no more than decomposing joint probabilities via basic probability rules to construct a linear equation set and subsequently solving the equations. Compared to the full-dimensional histogram (FDH) sanitization, CIPHER has drastic\-ally lower requirements on computa…
University of Vermont（佛蒙特大学）；MassMutual（万通互惠）；Raytheon（雷神公司）
Federated machine learning leverages edge computing to develop models from network user data, but privacy in federated learning remains a major challenge. Techniques using differential privacy have been proposed to address this, but bring their own challenges -- many require a trusted third party or else add too much noise to produce useful models. Recent advances in \emph{secure aggregation} using multiparty computation eliminate the need for a third party, but are computationally expensive especially at scale. We present a new federated learning protocol that leverages a novel differentially…
Boston University（波士顿大学）；Centrum Wiskunde & Informatica（荷兰国家数学与计算机科学研究所）；Microsoft Research（微软研究院）
Correlation clustering is a widely used technique in unsupervised machine learning. Motivated by applications where individual privacy is a concern, we initiate the study of differentially private correlation clustering. We propose an algorithm that achieves subquadratic additive error compared to the optimal cost. In contrast, straightforward adaptations of existing non-private algorithms all lead to a trivial quadratic error. Finally, we give a lower bound showing that any pure differentially private algorithm for correlation clustering requires additive error of $Ω(n)$.
Northwest University（西北大学）；Macau University of Science and Technology（澳门科技大学）
In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by using the alternating direction method of multipliers (ADMM) algorithm. The theoretical results and empirical results that show the utility of the proposed methods are also provided.
We demonstrate that differentially private machine learning has not yet reached its "AlexNet moment" on many canonical vision tasks: linear models trained on handcrafted features significantly outperform end-to-end deep neural networks for moderate privacy budgets. To exceed the performance of handcrafted features, we show that private learning requires either much more private data, or access to features learned on public data from a similar domain. Our work introduces simple yet strong baselines for differentially private learning that can inform the evaluation of future progress in this are…
High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference
School of Statistics and Data Science, Shanghai University of Finance and Economics（上海金融学院统计与数据科学学院）；School of Statistics and Data Science, Southeast University（东南大学统计与数据科学学院）；School of Statistics and Data Science, Shanghai University of International Business and Economics（上海国际商务学院统计与数据科学学院）
Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
Differential privacy is a formal, mathematical definition of data privacy that has gained traction in academia, industry, and government. The task of correctly constructing differentially private algorithms is non-trivial, and mistakes have been made in foundational algorithms. Currently, there is no automated support for converting an existing, non-private program into a differentially private version. In this paper, we propose a technique for automatically learning an accurate and differentially private version of a given non-private program. We show how to solve this difficult program synth…
Differentially private synthetic data generation offers a recent solution to release analytically useful data while preserving the privacy of individuals in the data. In order to utilize these algorithms for public policy decisions, policymakers need an accurate understanding of these algorithms' comparative performance. Correspondingly, data practitioners require standard metrics for evaluating the analytic qualities of the synthetic data. In this paper, we present an in-depth evaluation of several differentially private synthetic data algorithms using actual differentially private synthetic …
Learning from continuous data streams via classification/regression is prevalent in many domains. Adapting to evolving data characteristics (concept drift) while protecting data owners' private information is an open challenge. We present a differentially private ensemble solution to this problem with two distinguishing features: it allows an \textit{unbounded} number of ensemble updates to deal with the potentially never-ending data streams under a fixed privacy budget, and it is \textit{model agnostic}, in that it treats any pre-trained differentially private classification/regression model …
The Pennsylvania State University（宾夕法尼亚州立大学）；University of Georgia（佐治亚大学）
The process of data mining with differential privacy produces results that are affected by two types of noise: sampling noise due to data collection and privacy noise that is designed to prevent the reconstruction of sensitive information. In this paper, we consider the problem of designing confidence intervals for the parameters of a variety of differentially private machine learning models. The algorithms can provide confidence intervals that satisfy differential privacy (as well as the more recently proposed concentrated differential privacy) and can be used with existing differentially pri…
Khoury College of Computer Sciences, Northeastern University（东北大学胡里计算机科学学院）
We study the problem of differentially private constrained maximization of decomposable submodular functions. A submodular function is decomposable if it takes the form of a sum of submodular functions. The special case of maximizing a monotone, decomposable submodular function under cardinality constraints is known as the Combinatorial Public Projects (CPP) problem [Papadimitriou et al., 2008]. Previous work by Gupta et al. [2010] gave a differentially private algorithm for the CPP problem. We extend this work by designing differentially private algorithms for both monotone and non-monotone d…
Google Research（谷歌研究院）；Blavatnik School of Computer Science, Tel Aviv University（特拉维夫大学布拉瓦特尼克计算机科学学院）；Ben-Gurion University（本-古里安大学）
Clustering is a fundamental problem in data analysis. In differentially private clustering, the goal is to identify $k$ cluster centers without disclosing information on individual data points. Despite significant research progress, the problem had so far resisted practical solutions. In this work we aim at providing simple implementable differentially private clustering algorithms that provide utility when the data is "easy," e.g., when there exists a significant separation between the clusters. We propose a framework that allows us to apply non-private clustering algorithms to the easy insta…
We revisit the problem of $n$-gram extraction in the differential privacy setting. In this problem, given a corpus of private text data, the goal is to release as many $n$-grams as possible while preserving user level privacy. Extracting $n$-grams is a fundamental subroutine in many NLP applications such as sentence completion, response generation for emails etc. The problem also arises in other applications such as sequence mining, and is a generalization of recently studied differentially private set union (DPSU). In this paper, we develop a new differentially private algorithm for this prob…
Machine learning practitioners frequently seek to leverage the most informative available data, without violating the data owner's privacy, when building predictive models. Differentially private data synthesis protects personal details from exposure, and allows for the training of differentially private machine learning models on privately generated datasets. But how can we effectively assess the efficacy of differentially private synthetic data? In this paper, we survey four differentially private generative adversarial networks for data synthesis. We evaluate each of them at scale on five s…
We explore the training of generative adversarial networks with differential privacy to anonymize image data sets. On MNIST, we numerically measure the privacy-utility trade-off using parameters from $ε$-$δ$ differential privacy and the inception score. Our experiments uncover a saturated training regime where an increasing privacy budget adds little to the quality of generated images. We also explain analytically why differentially private Adam optimization is independent of the gradient clipping parameter. Furthermore, we highlight common errors in previous works on differentially private de…
Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we present a differentially private analogue of the classic Wilcoxon signed-rank hypothesis test, which is used when comparing sets of paired (e.g., before-and-after) data values. We present not only a private estimate of the test statistic, but a method to accurately compute a p-value and assess statistical significance. We evaluate our test on both simulated and real data. Compared to the only existing private test for this situation, that of Task and Clifton, we …
We study the problem of estimating high dimensional models with underlying sparse structures while preserving the privacy of each training example. We develop a differentially private high-dimensional sparse learning framework using the idea of knowledge transfer. More specifically, we propose to distill the knowledge from a "teacher" estimator trained on a private dataset, by creating a new dataset from auxiliary features, and then train a differentially private "student" estimator using this new dataset. In addition, we establish the linear convergence rate as well as the utility guarantee f…
Carnegie Mellon University（卡内基梅隆大学）；University of Pennsylvania（宾夕法尼亚大学）
This paper introduces the first provably accurate algorithms for differentially private, top-down decision tree learning in the distributed setting (Balcan et al., 2012). We propose DP-TopDown, a general privacy preserving decision tree learning algorithm, and present two distributed implementations. Our first method NoisyCounts naturally extends the single machine algorithm by using the Laplace mechanism. Our second method LocalRNM significantly reduces communication and added noise by performing local optimization at each data holder. We provide the first utility guarantees for differentiall…
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所）；University of Helsinki（赫尔辛基大学）
We propose an algorithm for the adaptation of the learning rate for stochastic gradient descent (SGD) that avoids the need for validation set use. The idea for the adaptiveness comes from the technique of extrapolation: to get an estimate for the error against the gradient flow which underlies SGD, we compare the result obtained by one full step and two half-steps. The algorithm is applied in two separate frameworks: federated and differentially private learning. Using examples of deep neural networks we empirically show that the adaptive algorithm is competitive with manually tuned commonly u…
Georgia Institute of Technology（佐治亚理工学院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Point process models are of great importance in real world applications. In certain critical applications, estimation of point process models involves large amounts of sensitive personal data from users. Privacy concerns naturally arise which have not been addressed in the existing literature. To bridge this glaring gap, we propose the first general differentially private estimation procedure for point process models. Specifically, we take the Hawkes process as an example, and introduce a rigorous definition of differential privacy for event stream data based on a discretized representation of…
University of Oxford（牛津大学）；University of Warwick（华威大学）；Universitat Pompeu Fabra（庞培法布拉大学）；University of Kaiserslautern（凯泽斯劳滕大学）；German Research Centre for Artificial Intelligence (DFKI)（德国人工智能研究中心）
Increasing interest in privacy-preserving machine learning has led to new and evolved approaches for generating private synthetic data from undisclosed real data. However, mechanisms of privacy preservation can significantly reduce the utility of synthetic data, which in turn impacts downstream tasks such as learning predictive models or inference. We propose several re-weighting strategies using privatised likelihood ratios that not only mitigate statistical bias of downstream estimators but also have general applicability to differentially private generative models. Through large-scale empir…
College of Information and Computer Sciences（信息与计算机科学学院）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
The study of private inference has been sparked by growing concern regarding the analysis of data when it stems from sensitive sources. We present the first method for private Bayesian inference in exponential families that properly accounts for noise introduced by the privacy mechanism. It is efficient because it works only with sufficient statistics and not individual data. Unlike other methods, it gives properly calibrated posterior beliefs in the non-asymptotic data regime.
Tsinghua University（清华大学）；Harvard University（哈佛大学）；University of California, Berkeley（加州大学伯克利分校）；Huazhong University of Science and Technology（华中科技大学）；Virginia Tech（弗吉尼亚理工大学）
Deep learning techniques have achieved remarkable performance in wide-ranging tasks. However, when trained on privacy-sensitive datasets, the model parameters may expose private information in training data. Prior attempts for differentially private training, although offering rigorous privacy guarantees, lead to much lower model performance than the non-private ones. Besides, different runs of the same training algorithm produce models with large performance variance. To address these issues, we propose DPlis--Differentially Private Learning wIth Smoothing. The core idea of DPlis is to constr…
Columbia University（哥伦比亚大学）；NTUA（雅典国立技术大学）；Northeastern University（东北大学）
We provide computationally efficient, differentially private algorithms for the classical regression settings of Least Squares Fitting, Binary Regression and Linear Regression with unbounded covariates. Prior to our work, privacy constraints in such regression settings were studied under strong a priori bounds on covariates. We consider the case of Gaussian marginals and extend recent differentially private techniques on mean and covariance estimation (Kamath et al., 2019; Karwa and Vadhan, 2018) to the sub-gaussian regime. We provide a novel technical analysis yielding differentially private …
University of California, Irvine（加州大学欧文分校）；Princeton University（普林斯顿大学）
Language modeling is a keystone task in natural language processing. When training a language model on sensitive information, differential privacy (DP) allows us to quantify the degree to which our private data is protected. However, training algorithms which enforce differential privacy often lead to degradation in model quality. We study the feasibility of learning a language model which is simultaneously high-quality and privacy preserving by tuning a public base model on a private corpus. We find that DP fine-tuning boosts the performance of language models in the private domain, making th…
We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially the same approximation ratios as those that can be obtained by any non-private algorithm, while incurring only small additive errors. This improves upon existing efficient algorithms that only achieve some large constant approximation factors. Our results also imply an improved algorithm for the Sample and Aggregate privacy framework. Furthermore, we show tha…
University of Houston（休斯顿大学）；Beijing University of Posts and Telecommunications（北京邮电大学）；University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）；University of Science and Technology of China（中国科学技术大学）
Due to massive amounts of data distributed across multiple locations, distributed machine learning has attracted a lot of research interests. Alternating Direction Method of Multipliers (ADMM) is a powerful method of designing distributed machine learning algorithm, whereby each agent computes over local datasets and exchanges computation results with its neighbor agents in an iterative procedure. There exists significant privacy leakage during this iterative process if the local data is sensitive. In this paper, we propose a differentially private ADMM algorithm (P-ADMM) to provide dynamic ze…
A common pain point in differentially private machine learning is the significant runtime overhead incurred when executing Differentially Private Stochastic Gradient Descent (DPSGD), which may be as large as two orders of magnitude. We thoroughly demonstrate that by exploiting powerful language primitives, including vectorization, just-in-time compilation, and static graph optimization, one can dramatically reduce these overheads, in many cases nearly matching the best non-private running times. These gains are realized in two frameworks: JAX and TensorFlow. JAX provides rich support for these…
In this note, we describe a simple approach to obtain a differentially private algorithm for k-clustering with nearly the same multiplicative factor as any non-private counterpart at the cost of a large polynomial additive error. The approach is the combination of a simple geometric observation independent of privacy consideration and any existing private algorithm with a constant approximation.
Columbia University, Department of Statistics（哥伦比亚大学统计系）；ENSAE ParisTech, Department of Statistics（巴黎高等经济商业学院统计系）
We derive concentration inequalities for differentially private median and mean estimators building on the "Propose, Test, Release" (PTR) mechanism introduced by Dwork and Lei (2009). We introduce a new general version of the PTR mechanism that allows us to derive high probability error bounds for differentially private estimators. Our algorithms provide the first statistical guarantees for differentially private estimation of the median and mean without any boundedness assumptions on the data, and without assuming that the target population parameter lies in some known bounded interval. Our p…
In this paper we tackle the challenge of making the stochastic coordinate descent algorithm differentially private. Compared to the classical gradient descent algorithm where updates operate on a single model vector and controlled noise addition to this vector suffices to hide critical information about individuals, stochastic coordinate descent crucially relies on keeping auxiliary information in memory during training. This auxiliary information provides an additional privacy leak and poses the major challenge addressed in this work. Driven by the insight that under independent noise additio…
