arXiv subjects

Jonathan Ullman

Publications and source records attributed to Jonathan Ullman.

At least 37 records · Page 2Linked to original sources

arXiv2023

SNAP: Efficient Extraction of Private Properties with Poisoning

Property inference attacks allow an adversary to extract global properties of the training dataset from a machine learning model. Such attacks have privacy implications for data owners sharing their datasets to train machine learning models. Several existing approaches for property inference attacks against deep neural networks have been proposed, but they all rely on the attacker training a large number of shadow models, which induces a large computational overhead. In this paper, we consider the setting of property inference attacks in which the attacker can poison a subset of the training dataset and query the trained target model. Motivated by our theoretical analysis of model confidences under poisoning, we design an efficient property inference attack, SNAP, which obtains higher attack success and requires lower amounts of poisoning than the state-of-the-art poisoning-based property inference attack by Mahloujifar et al. For example, on the Census dataset, SNAP achieves 34% higher success rate than Mahloujifar et al. while being 56.5x faster. We also extend our attack to infer whether a certain property was present at all during training and estimate the exact proportion of a property of interest efficiently. We evaluate our attack on several properties of varying proportions from four datasets and demonstrate SNAP's generality and effectiveness. An open-source implementation of SNAP can be found at https://github.com/johnmath/snap-sp23.

cs.LG↗

arXiv2023

Differentially Private Medians and Interior Points for Non-Pathological Data

We construct differentially private estimators with low sample complexity that estimate the median of an arbitrary distribution over $\mathbb{R}$ satisfying very mild moment conditions. Our result stands in contrast to the surprising negative result of Bun et al. (FOCS 2015) that showed there is no differentially private estimator with any finite sample complexity that returns any non-trivial approximation to the median of an arbitrary distribution.

cs.DS↗

arXiv2023

From Robustness to Privacy and Back

We study the relationship between two desiderata of algorithms in statistical inference and machine learning: differential privacy and robustness to adversarial data corruptions. Their conceptual similarity was first observed by Dwork and Lei (STOC 2009), who observed that private algorithms satisfy robustness, and gave a general method for converting robust algorithms to private ones. However, all general methods for transforming robust algorithms into private ones lead to suboptimal error rates. Our work gives the first black-box transformation that converts any adversarially robust algorithm into one that satisfies pure differential privacy. Moreover, we show that for any low-dimensional estimation task, applying our transformation to an optimal robust estimator results in an optimal private estimator. Thus, we conclude that for any low-dimensional task, the optimal error rate for $\varepsilon$-differentially private estimators is essentially the same as the optimal error rate for estimators that are robust to adversarially corrupting $1/\varepsilon$ training samples. We apply our transformation to obtain new optimal private estimators for several high-dimensional tasks, including Gaussian (sparse) linear regression and PCA. Finally, we present an extension of our transformation that leads to approximate differentially private algorithms whose error does not depend on the range of the output space, which is impossible under pure differential privacy.

cs.LG↗

arXiv2022

Fair and Optimal Cohort Selection for Linear Utilities

The rise of algorithmic decision-making has created an explosion of research around the fairness of those algorithms. While there are many compelling notions of individual fairness, beginning with the work of Dwork et al., these notions typically do not satisfy desirable composition properties. To this end, Dwork and Ilvento introduced the fair cohort selection problem, which captures a specific application where a single fair classifier is composed with itself to pick a group of candidates of size exactly $k$. In this work we introduce a specific instance of cohort selection where the goal is to choose a cohort maximizing a linear utility function. We give approximately optimal polynomial-time algorithms for this problem in both an offline setting where the entire fair classifier is given at once, or an online setting where candidates arrive one at a time and are classified as they arrive.

cs.DS↗

arXiv2022

Multitask Learning via Shared Features: Algorithms and Hardness

We investigate the computational efficiency of multitask learning of Boolean functions over the $d$-dimensional hypercube, that are related by means of a feature representation of size $k \ll d$ shared across all tasks. We present a polynomial time multitask learning algorithm for the concept class of halfspaces with margin $γ$, which is based on a simultaneous boosting technique and requires only $\textrm{poly}(k/γ)$ samples-per-task and $\textrm{poly}(k\log(d)/γ)$ samples in total. In addition, we prove a computational separation, showing that assuming there exists a concept class that cannot be learned in the attribute-efficient model, we can construct another concept class such that can be learned in the attribute-efficient model, but cannot be multitask learned efficiently -- multitask learning this concept class either requires super-polynomial time complexity or a much larger total number of samples.

cs.LG↗

arXiv2022

How to Combine Membership-Inference Attacks on Multiple Updated Models

A large body of research has shown that machine learning models are vulnerable to membership inference (MI) attacks that violate the privacy of the participants in the training data. Most MI research focuses on the case of a single standalone model, while production machine-learning platforms often update models over time, on data that often shifts in distribution, giving the attacker more information. This paper proposes new attacks that take advantage of one or more model updates to improve MI. A key part of our approach is to leverage rich information from standalone MI attacks mounted separately against the original and updated models, and to combine this information in specific ways to improve attack effectiveness. We propose a set of combination functions and tuning methods for each, and present both analytical and quantitative justification for various options. Our results on four public datasets show that our attacks are effective at using update information to give the adversary a significant advantage over attacks on standalone models, but also compared to a prior MI attack that takes advantage of model updates in a related machine-unlearning setting. We perform the first measurements of the impact of distribution shift on MI attacks with model updates, and show that a more drastic distribution shift results in significantly higher MI risk than a gradual shift. Our code is available at https://www.github.com/stanleykywu/model-updates.

cs.LG↗

arXiv2022

Fair and Useful Cohort Selection

A challenge in fair algorithm design is that, while there are compelling notions of individual fairness, these notions typically do not satisfy desirable composition properties, and downstream applications based on fair classifiers might not preserve fairness. To study fairness under composition, Dwork and Ilvento introduced an archetypal problem called fair-cohort-selection problem, where a single fair classifier is composed with itself to select a group of candidates of a given size, and proposed a solution to this problem. In this work we design algorithms for selecting cohorts that not only preserve fairness, but also maximize the utility of the selected cohort under two notions of utility that we introduce and motivate. We give optimal (or approximately optimal) polynomial-time algorithms for this problem in both an offline setting, and an online setting where candidates arrive one at a time and are classified as they arrive.

cs.DS↗

arXiv2022

Private Identity Testing for High-Dimensional Distributions

In this work we present novel differentially private identity (goodness-of-fit) testers for natural and widely studied classes of multivariate product distributions: Gaussians in $\mathbb{R}^d$ with known covariance and product distributions over $\{\pm 1\}^{d}$. Our testers have improved sample complexity compared to those derived from previous techniques, and are the first testers whose sample complexity matches the order-optimal minimax sample complexity of $O(d^{1/2}/α^2)$ in many parameter regimes. We construct two types of testers, exhibiting tradeoffs between sample complexity and computational complexity. Finally, we provide a two-way reduction between testing a subclass of multivariate product distributions and testing univariate distributions, and thereby obtain upper and lower bounds for testing this subclass of product distributions.

cs.DS↗

arXiv2022

A Private and Computationally-Efficient Estimator for Unbounded Gaussians

We give the first polynomial-time, polynomial-sample, differentially private estimator for the mean and covariance of an arbitrary Gaussian distribution $\mathcal{N}(μ,Σ)$ in $\mathbb{R}^d$. All previous estimators are either nonconstructive, with unbounded running time, or require the user to specify a priori bounds on the parameters $μ$ and $Σ$. The primary new technical tool in our algorithm is a new differentially private preconditioner that takes samples from an arbitrary Gaussian $\mathcal{N}(0,Σ)$ and returns a matrix $A$ such that $A ΣA^T$ has constant condition number.

stat.ML↗

arXiv2021

Privacy Odometers and Filters: Pay-as-you-Go Composition

In this paper we initiate the study of adaptive composition in differential privacy when the length of the composition, and the privacy parameters themselves can be chosen adaptively, as a function of the outcome of previously run analyses. This case is much more delicate than the setting covered by existing composition theorems, in which the algorithms themselves can be chosen adaptively, but the privacy parameters must be fixed up front. Indeed, it isn't even clear how to define differential privacy in the adaptive parameter setting. We proceed by defining two objects which cover the two main use cases of composition theorems. A privacy filter is a stopping time rule that allows an analyst to halt a computation before his pre-specified privacy budget is exceeded. A privacy odometer allows the analyst to track realized privacy loss as he goes, without needing to pre-specify a privacy budget. We show that unlike the case in which privacy parameters are fixed, in the adaptive parameter setting, these two use cases are distinct. We show that there exist privacy filters with bounds comparable (up to constants) with existing privacy composition theorems. We also give a privacy odometer that nearly matches non-adaptive private composition theorems, but is sometimes worse by a small asymptotic factor. Moreover, we show that this is inherent, and that any valid privacy odometer in the adaptive parameter setting must lose this factor, which shows a formal separation between the filter and odometer use-cases.

cs.CR↗

arXiv2021

Leveraging Public Data for Practical Private Query Release

In many statistical problems, incorporating priors can significantly improve performance. However, the use of prior knowledge in differentially private query release has remained underexplored, despite such priors commonly being available in the form of public datasets, such as previous US Census releases. With the goal of releasing statistics about a private dataset, we present PMW^Pub, which -- unlike existing baselines -- leverages public data drawn from a related distribution as prior information. We provide a theoretical analysis and an empirical evaluation on the American Community Survey (ACS) and ADULT datasets, which shows that our method outperforms state-of-the-art methods. Furthermore, PMW^Pub scales well to high-dimensional data domains, where running many existing methods would be computationally infeasible.

cs.LG↗

arXiv2021

Tight Lower Bounds for Locally Differentially Private Selection

We prove a tight lower bound (up to constant factors) on the sample complexity of any non-interactive local differentially private protocol for optimizing a linear function over the simplex. This lower bound also implies a tight lower bound (again, up to constant factors) on the sample complexity of any non-interactive local differentially private protocol implementing the exponential mechanism. These results reveal that any local protocol for these problems has exponentially worse dependence on the dimension than corresponding algorithms in the central model. Previously, Kasiviswanathan et al. (FOCS 2008) proved an exponential separation between local and central model algorithms for PAC learning the class of parity functions. In contrast, our lower bound are quantitatively tight, apply to a simple and natural class of linear optimization problems, and our techniques are arguably simpler.

cs.CR↗

arXiv2021

Private Mean Estimation of Heavy-Tailed Distributions

We give new upper and lower bounds on the minimax sample complexity of differentially private mean estimation of distributions with bounded $k$-th moments. Roughly speaking, in the univariate case, we show that $n = Θ\left(\frac{1}{α^2} + \frac{1}{α^{\frac{k}{k-1}}\varepsilon}\right)$ samples are necessary and sufficient to estimate the mean to $α$-accuracy under $\varepsilon$-differential privacy, or any of its common relaxations. This result demonstrates a qualitatively different behavior compared to estimation absent privacy constraints, for which the sample complexity is identical for all $k \geq 2$. We also give algorithms for the multivariate setting whose sample complexity is a factor of $O(d)$ larger than the univariate case.

cs.DS↗

arXiv2020

The Limits of Pan Privacy and Shuffle Privacy for Learning and Estimation

There has been a recent wave of interest in intermediate trust models for differential privacy that eliminate the need for a fully trusted central data collector, but overcome the limitations of local differential privacy. This interest has led to the introduction of the shuffle model (Cheu et al., EUROCRYPT 2019; Erlingsson et al., SODA 2019) and revisiting the pan-private model (Dwork et al., ITCS 2010). The message of this line of work is that, for a variety of low-dimensional problems -- such as counts, means, and histograms -- these intermediate models offer nearly as much power as central differential privacy. However, there has been considerably less success using these models for high-dimensional learning and estimation problems. In this work, we show that, for a variety of high-dimensional learning and estimation problems, both the shuffle model and the pan-private model inherently incur an exponential price in sample complexity relative to the central model. For example, we show that, private agnostic learning of parity functions over $d$ bits requires $Ω(2^{d/2})$ samples in these models, and privately selecting the most common attribute from a set of $d$ choices requires $Ω(d^{1/2})$ samples, both of which are exponential separations from the central model. Our work gives the first non-trivial lower bounds for these problems for both the pan-private model and the general multi-message shuffle model.

cs.DS↗

arXiv2020

Auditing Differentially Private Machine Learning: How Private is Private SGD?

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 implementations of differentially private algorithms that we believe has the potential to complement and influence analytical work on differential privacy.

cs.CR↗

arXiv2020

A Primer on Private Statistics

Differentially private statistical estimation has seen a flurry of developments over the last several years. Study has been divided into two schools of thought, focusing on empirical statistics versus population statistics. We suggest that these two lines of work are more similar than different by giving examples of methods that were initially framed for empirical statistics, but can be applied just as well to population statistics. We also provide a thorough coverage of recent work in this area.

stat.ML↗

arXiv2020

Private Query Release Assisted by Public Data

We study the problem of differentially private query release assisted by access to public data. In this problem, the goal is to answer a large class $\mathcal{H}$ of statistical queries with error no more than $α$ using a combination of public and private samples. The algorithm is required to satisfy differential privacy only with respect to the private samples. We study the limits of this task in terms of the private and public sample complexities. First, we show that we can solve the problem for any query class $\mathcal{H}$ of finite VC-dimension using only $d/α$ public samples and $\sqrt{p}d^{3/2}/α^2$ private samples, where $d$ and $p$ are the VC-dimension and dual VC-dimension of $\mathcal{H}$, respectively. In comparison, with only private samples, this problem cannot be solved even for simple query classes with VC-dimension one, and without any private samples, a larger public sample of size $d/α^2$ is needed. Next, we give sample complexity lower bounds that exhibit tight dependence on $p$ and $α$. For the class of decision stumps, we give a lower bound of $\sqrt{p}/α$ on the private sample complexity whenever the public sample size is less than $1/α^2$. Given our upper bounds, this shows that the dependence on $\sqrt{p}$ is necessary in the private sample complexity. We also give a lower bound of $1/α$ on the public sample complexity for a broad family of query classes, which by our upper bound, is tight in $α$.

cs.LG↗

arXiv2020

Efficient Private Algorithms for Learning Large-Margin Halfspaces

We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex optimization, the sample complexity of our algorithms depends only on the margin of the data, and not on the dimension. We complement our results with a lower bound, showing that the dependence of our upper bounds on the margin is optimal.

cs.LG↗