We study the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) with heavy-tailed data. Specifically, we focus on the $\ell_1$-norm linear regression in the $ε$-DP model. While most of the previous work focuses on the case where the loss function is Lipschitz, here we only need to assume the variates has bounded moments. Firstly, we study the case where the $\ell_2$ norm of data has bounded second order moment. We propose an algorithm which is based on the exponential mechanism and show that it is possible to achieve an upper bound of $\tilde{O}(\sqrt{\frac{d}{nε}})$ (with high probability). Next, we relax the assumption to bounded $θ$-th order moment with some $θ\in (1, 2)$ and show that it is possible to achieve an upper bound of $\tilde{O}(({\frac{d}{nε}})^\frac{θ-1}θ)$. Our algorithms can also be extended to more relaxed cases where only each coordinate of the data has bounded moments, and we can get an upper bound of $\tilde{O}({\frac{d}{\sqrt{nε}}})$ and $\tilde{O}({\frac{d}{({nε})^\frac{θ-1}θ}})$ in the second and $θ$-th moment case respectively.
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…
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 …
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…
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…
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…
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…
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…
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…
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.
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 Waterloo（滑铁卢大学）；Meta；Cornell University（康奈尔大学）
We study stochastic convex optimization with heavy-tailed data under the constraint of differential privacy (DP). Most prior work on this problem is restricted to the case where the loss function is Lipschitz. Instead, as introduced by Wang, Xiao, Devadas, and Xu \cite{WangXDX20}, we study general convex loss functions with the assumption that the distribution of gradients has bounded $k$-th moments. We provide improved upper bounds on the excess population risk under concentrated DP for convex and strongly convex loss functions. Along the way, we derive new algorithms for private mean estimat…
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…
Catastrophic forgetting can be a significant problem for institutions that must delete historic data for privacy reasons. For example, hospitals might not be able to retain patient data permanently. But neural networks trained on recent data alone will tend to forget lessons learned on old data. We present a differentially private continual learning framework based on variational inference. We estimate the likelihood of past data given the current model using differentially private generative models of old datasets.
We propose the differentially private lottery ticket mechanism (DPLTM). An end-to-end differentially private training paradigm based on the lottery ticket hypothesis. Using "high-quality winners", selected via our custom score function, DPLTM significantly improves the privacy-utility trade-off over the state-of-the-art. We show that DPLTM converges faster, allowing for early stopping with reduced privacy budget consumption. We further show that the tickets from DPLTM are transferable across datasets, domains, and architectures. Our extensive evaluation on several public datasets provides evid…
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.
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所（HIIT））；Aalto University（阿尔托大学）；University of Helsinki（赫尔辛基大学）
Motivation: Human genomic datasets often contain sensitive information that limits use and sharing of the data. In particular, simple anonymisation strategies fail to provide sufficient level of protection for genomic data, because the data are inherently identifiable. Differentially private machine learning can help by guaranteeing that the published results do not leak too much information about any individual data point. Recent research has reached promising results on differentially private drug sensitivity prediction using gene expression data. Differentially private learning with genomic…
In this paper, we study the differentially private empirical risk minimization problem where the parameter is constrained to a Riemannian manifold. We introduce a framework of differentially private Riemannian optimization by adding noise to the Riemannian gradient on the tangent space. The noise follows a Gaussian distribution intrinsically defined with respect to the Riemannian metric. We adapt the Gaussian mechanism from the Euclidean space to the tangent space compatible to such generalized Gaussian distribution. We show that this strategy presents a simple analysis as compared to directly…
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…
We study differentially private mean estimation in a high-dimensional setting. Existing differential privacy techniques applied to large dimensions lead to computationally intractable problems or estimators with excessive privacy loss. Recent work in high-dimensional robust statistics has identified computationally tractable mean estimation algorithms with asymptotic dimension-independent error guarantees. We incorporate these results to develop a strict bound on the global sensitivity of the robust mean estimator. This yields a computationally tractable algorithm for differentially private me…
Tel Aviv University（特拉维夫大学）；Google（谷歌）；Ben-Gurion University（本-古里安大学）
We present differentially private efficient algorithms for learning union of polygons in the plane (which are not necessarily convex). Our algorithms achieve $(α,β)$-PAC learning and $(ε,δ)$-differential privacy using a sample of size $\tilde{O}\left(\frac{1}{αε}k\log d\right)$, where the domain is $[d]\times[d]$ and $k$ is the number of edges in the union of polygons.
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…
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 $Ω(n)$.
We study the relationship between the notions of differentially private learning and online learning in games. Several recent works have shown that differentially private learning implies online learning, but an open problem of Neel, Roth, and Wu \cite{NeelAaronRoth2018} asks whether this implication is {\it efficient}. Specifically, does an efficient differentially private learner imply an efficient online learner? In this paper we resolve this open question in the context of pure differential privacy. We derive an efficient black-box reduction from differentially private learning to online l…
Media Lab（媒体实验室）；Institute for Data, Systems and Society（数据、系统与社会研究所）；Massachusetts Institute of Technology（麻省理工学院）
The rapid proliferation of decentralized learning systems mandates the need for differentially-private cooperative learning. In this paper, we study this in context of the contextual linear bandit: we consider a collection of agents cooperating to solve a common contextual bandit, while ensuring that their communication remains private. For this problem, we devise \textsc{FedUCB}, a multiagent private algorithm for both centralized and decentralized (peer-to-peer) federated learning. We provide a rigorous technical analysis of its utility in terms of regret, improving several results in cooper…
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].
Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as sample complexity for learning the parameters and releasing differentially private versions, are yet to be thoroughly analyzed. In this work, we study standard Hawkes processes with background intensity $μ$ and excitation function $αe^{-βt}$. We provide both non-private and differentially private estimators of $μ$ and $α$, and obtain sample complexity results in …
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…
National University of Singapore（新加坡国立大学）；The University of Melbourne（墨尔本大学）；IBM Singapore Lab（IBM新加坡实验室）；Monash University（莫纳什大学）；Deakin University（迪肯大学）
This paper firstly considers the research problem of fairness in collaborative deep learning, while ensuring privacy. A novel reputation system is proposed through digital tokens and local credibility to ensure fairness, in combination with differential privacy to guarantee privacy. In particular, we build a fair and differentially private decentralised deep learning framework called FDPDDL, which enables parties to derive more accurate local models in a fair and private manner by using our developed two-stage scheme: during the initialisation stage, artificial samples generated by Differentia…
University of Chicago（芝加哥大学）；Toyota Technological Institute at Chicago（芝加哥丰田工业大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
We propose an adaptive (stochastic) gradient perturbation method for differentially private empirical risk minimization. At each iteration, the random noise added to the gradient is optimally adapted to the stepsize; we name this process adaptive differentially private (ADP) learning. Given the same privacy budget, we prove that the ADP method considerably improves the utility guarantee compared to the standard differentially private method in which vanilla random noise is added. Our method is particularly useful for gradient-based algorithms with time-varying learning rates, including variant…
Survival function estimation is used in many disciplines, but it is most common in medical analytics in the form of the Kaplan-Meier estimator. Sensitive data (patient records) is used in the estimation without any explicit control on the information leakage, which is a significant privacy concern. We propose a first differentially private estimator of the survival function and show that it can be easily extended to provide differentially private confidence intervals and test statistics without spending any extra privacy budget. We further provide extensions for differentially private estimati…
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 …
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…
Differential privacy is concerned about the prediction quality while measuring the privacy impact on individuals whose information is contained in the data. We consider differentially private risk minimization problems with regularizers that induce structured sparsity. These regularizers are known to be convex but they are often non-differentiable. We analyze the standard differentially private algorithms, such as output perturbation, Frank-Wolfe and objective perturbation. Output perturbation is a differentially private algorithm that is known to perform well for minimizing risks that are str…
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…
Linear regression is an important tool across many fields that work with sensitive human-sourced data. Significant prior work has focused on producing differentially private point estimates, which provide a privacy guarantee to individuals while still allowing modelers to draw insights from data by estimating regression coefficients. We investigate the problem of Bayesian linear regression, with the goal of computing posterior distributions that correctly quantify uncertainty given privately released statistics. We show that a naive approach that ignores the noise injected by the privacy mecha…
