arXiv subjects

Or Sheffet

Publications and source records attributed to Or Sheffet.

At least 19 recordsLinked to original sources

arXiv2025

Differentially Private Learning of Exponential Distributions: Simple Algorithms and Tight Bounds

We study the problem of learning exponential distributions under differential privacy. Given $n$ i.i.d.\ samples from $\mathrm{Exp}(\lambda)$, the goal is to privately estimate $\lambda$ so that the learned distribution is close in total variation distance to the truth. We present a simple pure $\epsilon$-differentially private algorithm that avoids the classical dependence on the true value of $\lambda$. Our method leverages a structural property of the exponential distribution: its $(1-1/e)$-quantile equals $1/\lambda$, allowing us to estimate the rate parameter directly via private quantile estimation. The resulting learner is both conceptually simple and sample-efficient, achieving near-optimal guarantees. We further extend the method to Pareto distributions via a logarithmic reduction, prove nearly matching lower bounds using group privacy arguments, and show how approximate $(\epsilon,\delta)$-DP removes the need for externally supplied parameter bounds. Together, these results give the first tight characterization of exponential distribution learning under differential privacy using a simple $\lambda$-free approach.

cs.DS↗

arXiv2025

Privacy-Preserving Conformal Prediction Under Local Differential Privacy

Conformal prediction (CP) provides sets of candidate classes with a guaranteed probability of containing the true class. However, it typically relies on a calibration set with clean labels. We address privacy-sensitive scenarios where the aggregator is untrusted and can only access a perturbed version of the true labels. We propose two complementary approaches under local differential privacy (LDP). In the first approach, users do not access the model but instead provide their input features and a perturbed label using a k-ary randomized response. In the second approach, which enforces stricter privacy constraints, users add noise to their conformity score by binary search response. This method requires access to the classification model but preserves both data and label privacy. Both approaches compute the conformal threshold directly from noisy data without accessing the true labels. We prove finite-sample coverage guarantees and demonstrate robust coverage even under severe randomization. This approach unifies strong local privacy with predictive uncertainty control, making it well-suited for sensitive applications such as medical imaging or large language model queries, regardless of whether users can (or are willing to) compute their own scores.

cs.LG↗

arXiv2025

A Private Approximation of the 2nd-Moment Matrix of Any Subsamplable Input

We study the problem of differentially private second moment estimation and present a new algorithm that achieve strong privacy-utility trade-offs even for worst-case inputs under subsamplability assumptions on the data. We call an input $(m,\alpha,\beta)$-subsamplable if a random subsample of size $m$ (or larger) preserves w.p $\geq 1-\beta$ the spectral structure of the original second moment matrix up to a multiplicative factor of $1\pm \alpha$. Building upon subsamplability, we give a recursive algorithmic framework similar to Kamath et al 2019, that abides zero-Concentrated Differential Privacy (zCDP) while preserving w.h.p. the accuracy of the second moment estimation upto an arbitrary factor of $(1\pm\gamma)$. We then show how to apply our algorithm to approximate the second moment matrix of a distribution $\mathcal{D}$, even when a noticeable fraction of the input are outliers.

cs.LG↗

arXiv2022

A Differentially Private Linear-Time fPTAS for the Minimum Enclosing Ball Problem

The Minimum Enclosing Ball (MEB) problem is one of the most fundamental problems in clustering, with applications in operations research, statistics and computational geometry. In this works, we give the first differentially private (DP) fPTAS for the Minimum Enclosing Ball problem, improving both on the runtime and the utility bound of the best known DP-PTAS for the problem, of Ghazi et al. (2020). Given $n$ points in $\R^d$ that are covered by the ball $B(\theta_{opt},r_{opt})$, our simple iterative DP-algorithm returns a ball $B(\theta,r)$ where $r\leq (1+\gamma)r_{opt}$ and which leaves at most $\tilde O(\frac{\sqrt d}{\gamma\epsilon})$ points uncovered in $\tilde O(\nicefrac n {\gamma^2})$-time. We also give a local-model version of our algorithm, that leaves at most $\tilde O(\frac{\sqrt {nd}}{\gamma\epsilon})$ points uncovered, improving on the $n^{0.67}$-bound of Nissim and Stemmer (2018) (at the expense of other parameters). In addition, we test our algorithm empirically and discuss future open problems.

cs.DS↗

arXiv2022

Transfer Learning In Differential Privacy's Hybrid-Model

The hybrid-model (Avent et al 2017) in Differential Privacy is a an augmentation of the local-model where in addition to N local-agents we are assisted by one special agent who is in fact a curator holding the sensitive details of n additional individuals. Here we study the problem of machine learning in the hybrid-model where the n individuals in the curators dataset are drawn from a different distribution than the one of the general population (the local-agents). We give a general scheme -- Subsample-Test-Reweigh -- for this transfer learning problem, which reduces any curator-model DP-learner to a hybrid-model learner in this setting using iterative subsampling and reweighing of the n examples held by the curator based on a smooth variation of the Multiplicative-Weights algorithm (introduced by Bun et al, 2020). Our scheme has a sample complexity which relies on the chi-squared divergence between the two distributions. We give worst-case analysis bounds on the sample complexity required for our private reduction. Aiming to reduce said sample complexity, we give two specific instances our sample complexity can be drastically reduced (one instance is analyzed mathematically, while the other - empirically) and pose several directions for follow-up work.

cs.LG↗

arXiv2020

Private Approximations of a Convex Hull in Low Dimensions

We give the first differentially private algorithms that estimate a variety of geometric features of points in the Euclidean space, such as diameter, width, volume of convex hull, min-bounding box, min-enclosing ball etc. Our work relies heavily on the notion of \emph{Tukey-depth}. Instead of (non-privately) approximating the convex-hull of the given set of points $P$, our algorithms approximate the geometric features of the $\kappa$-Tukey region induced by $P$ (all points of Tukey-depth $\kappa$ or greater). Moreover, our approximations are all bi-criteria: for any geometric feature $\mu$ our $(\alpha,\Delta)$-approximation is a value "sandwiched" between $(1-\alpha)\mu(D_P(\kappa))$ and $(1+\alpha)\mu(D_P(\kappa-\Delta))$. Our work is aimed at producing a \emph{$(\alpha,\Delta)$-kernel of $D_P(\kappa)$}, namely a set $\mathcal{S}$ such that (after a shift) it holds that $(1-\alpha)D_P(\kappa)\subset \mathsf{CH}(\mathcal{S}) \subset (1+\alpha)D_P(\kappa-\Delta)$. We show that an analogous notion of a bi-critera approximation of a directional kernel, as originally proposed by Agarwal et al~[2004], \emph{fails} to give a kernel, and so we result to subtler notions of approximations of projections that do yield a kernel. First, we give differentially private algorithms that find $(\alpha,\Delta)$-kernels for a "fat" Tukey-region. Then, based on a private approximation of the min-bounding box, we find a transformation that does turn $D_P(\kappa)$ into a "fat" region \emph{but only if} its volume is proportional to the volume of $D_P(\kappa-\Delta)$. Lastly, we give a novel private algorithm that finds a depth parameter $\kappa$ for which the volume of $D_P(\kappa)$ is comparable to $D_P(\kappa-\Delta)$. We hope this work leads to the further study of the intersection of differential privacy and computational geometry.

cs.DS↗

arXiv2020

Quantile Multi-Armed Bandits: Optimal Best-Arm Identification and a Differentially Private Scheme

We study the best-arm identification problem in multi-armed bandits with stochastic, potentially private rewards, when the goal is to identify the arm with the highest quantile at a fixed, prescribed level. First, we propose a (non-private) successive elimination algorithm for strictly optimal best-arm identification, we show that our algorithm is $\delta$-PAC and we characterize its sample complexity. Further, we provide a lower bound on the expected number of pulls, showing that the proposed algorithm is essentially optimal up to logarithmic factors. Both upper and lower complexity bounds depend on a special definition of the associated suboptimality gap, designed in particular for the quantile bandit problem, as we show when the gap approaches zero, best-arm identification is impossible. Second, motivated by applications where the rewards are private, we provide a differentially private successive elimination algorithm whose sample complexity is finite even for distributions with infinite support-size, and we characterize its sample complexity. Our algorithms do not require prior knowledge of either the suboptimality gap or other statistical information related to the bandit problem at hand.

stat.ML↗

arXiv2019

The power of synergy in differential privacy: Combining a small curator with local randomizers

Motivated by the desire to bridge the utility gap between local and trusted curator models of differential privacy for practical applications, we initiate the theoretical study of a hybrid model introduced by "Blender" [Avent et al.,\ USENIX Security '17], in which differentially private protocols of n agents that work in the local-model are assisted by a differentially private curator that has access to the data of m additional users. We focus on the regime where m << n and study the new capabilities of this (m,n)-hybrid model. We show that, despite the fact that the hybrid model adds no significant new capabilities for the basic task of simple hypothesis-testing, there are many other tasks (under a wide range of parameters) that can be solved in the hybrid model yet cannot be solved either by the curator or by the local-users separately. Moreover, we exhibit additional tasks where at least one round of interaction between the curator and the local-users is necessary -- namely, no hybrid model protocol without such interaction can solve these tasks. Taken together, our results show that the combination of the local model with a small curator can become part of a promising toolkit for designing and implementing differential privacy.

cs.DS↗

arXiv2019

Differentially Private Algorithms for Learning Mixtures of Separated Gaussians

Learning the parameters of Gaussian mixture models is a fundamental and widely studied problem with numerous applications. In this work, we give new algorithms for learning the parameters of a high-dimensional, well separated, Gaussian mixture model subject to the strong constraint of differential privacy. In particular, we give a differentially private analogue of the algorithm of Achlioptas and McSherry. Our algorithm has two key properties not achieved by prior work: (1) The algorithm's sample complexity matches that of the corresponding non-private algorithm up to lower order terms in a wide range of parameters. (2) The algorithm does not require strong a priori bounds on the parameters of the mixture components.

cs.DS↗

arXiv2019

An Optimal Private Stochastic-MAB Algorithm Based on an Optimal Private Stopping Rule

We present a provably optimal differentially private algorithm for the stochastic multi-arm bandit problem, as opposed to the private analogue of the UCB-algorithm [Mishra and Thakurta, 2015; Tossou and Dimitrakakis, 2016] which doesn't meet the recently discovered lower-bound of $\Omega \left(\frac{K\log(T)}{\epsilon} \right)$ [Shariff and Sheffet, 2018]. Our construction is based on a different algorithm, Successive Elimination [Even-Dar et al. 2002], that repeatedly pulls all remaining arms until an arm is found to be suboptimal and is then eliminated. In order to devise a private analogue of Successive Elimination we visit the problem of private stopping rule, that takes as input a stream of i.i.d samples from an unknown distribution and returns a multiplicative $(1 \pm \alpha)$-approximation of the distribution's mean, and prove the optimality of our private stopping rule. We then present the private Successive Elimination algorithm which meets both the non-private lower bound [Lai and Robbins, 1985] and the above-mentioned private lower bound. We also compare empirically the performance of our algorithm with the private UCB algorithm.

stat.ML↗

arXiv2018

Locally Private Mean Estimation: Z-test and Tight Confidence Intervals

This work provides tight upper- and lower-bounds for the problem of mean estimation under $\epsilon$-differential privacy in the local model, when the input is composed of $n$ i.i.d. drawn samples from a normal distribution with variance $\sigma$. Our algorithms result in a $(1-\beta)$-confidence interval for the underlying distribution's mean $\mu$ of length $\tilde O\left( \frac{\sigma \sqrt{\log(\frac 1 \beta)}}{\epsilon\sqrt n} \right)$. In addition, our algorithms leverage binary search using local differential privacy for quantile estimation, a result which may be of separate interest. Moreover, we prove a matching lower-bound (up to poly-log factors), showing that any one-shot (each individual is presented with a single query) local differentially private algorithm must return an interval of length $\Omega\left( \frac{\sigma\sqrt{\log(1/\beta)}}{\epsilon\sqrt{n}}\right)$.

cs.DS↗

arXiv2018

Differentially Private Contextual Linear Bandits

We study the contextual linear bandit problem, a version of the standard stochastic multi-armed bandit (MAB) problem where a learner sequentially selects actions to maximize a reward which depends also on a user provided per-round context. Though the context is chosen arbitrarily or adversarially, the reward is assumed to be a stochastic function of a feature vector that encodes the context and selected action. Our goal is to devise private learners for the contextual linear bandit problem. We first show that using the standard definition of differential privacy results in linear regret. So instead, we adopt the notion of joint differential privacy, where we assume that the action chosen on day $t$ is only revealed to user $t$ and thus needn't be kept private that day, only on following days. We give a general scheme converting the classic linear-UCB algorithm into a joint differentially private algorithm using the tree-based algorithm. We then apply either Gaussian noise or Wishart noise to achieve joint-differentially private algorithms and bound the resulting algorithms' regrets. In addition, we give the first lower bound on the additional regret any private algorithms for the MAB problem must incur.

cs.LG↗

arXiv2018

Locally Private Hypothesis Testing

We initiate the study of differentially private hypothesis testing in the local-model, under both the standard (symmetric) randomized-response mechanism (Warner, 1965, Kasiviswanathan et al, 2008) and the newer (non-symmetric) mechanisms (Bassily and Smith, 2015, Bassily et al, 2017). First, we study the general framework of mapping each user's type into a signal and show that the problem of finding the maximum-likelihood distribution over the signals is feasible. Then we discuss the randomized-response mechanism and show that, in essence, it maps the null- and alternative-hypotheses onto new sets, an affine translation of the original sets. We then give sample complexity bounds for identity and independence testing under randomized-response. We then move to the newer non-symmetric mechanisms and show that there too the problem of finding the maximum-likelihood distribution is feasible. Under the mechanism of Bassily et al (2007) we give identity and independence testers with better sample complexity than the testers in the symmetric case, and we also propose a $\chi^2$-based identity tester which we investigate empirically.

cs.CR↗

arXiv2015

Differentially Private Ordinary Least Squares

Linear regression is one of the most prevalent techniques in machine learning, however, it is also common to use linear regression for its \emph{explanatory} capabilities rather than label prediction. Ordinary Least Squares (OLS) is often used in statistics to establish a correlation between an attribute (e.g. gender) and a label (e.g. income) in the presence of other (potentially correlated) features. OLS assumes a particular model that randomly generates the data, and derives \emph{$t$-values} --- representing the likelihood of each real value to be the true correlation. Using $t$-values, OLS can release a \emph{confidence interval}, which is an interval on the reals that is likely to contain the true correlation, and when this interval does not intersect the origin, we can \emph{reject the null hypothesis} as it is likely that the true correlation is non-zero. Our work aims at achieving similar guarantees on data under differentially private estimators. First, we show that for well-spread data, the Gaussian Johnson-Lindenstrauss Transform (JLT) gives a very good approximation of $t$-values, secondly, when JLT approximates Ridge regression (linear regression with $l_2$-regularization) we derive, under certain conditions, confidence intervals using the projected data, lastly, we derive, under different conditions, confidence intervals for the "Analyze Gauss" algorithm (Dwork et al, STOC 2014).

cs.DS↗

arXiv2015

Private Approximations of the 2nd-Moment Matrix Using Existing Techniques in Linear Regression

We introduce three differentially-private algorithms that approximates the 2nd-moment matrix of the data. These algorithm, which in contrast to existing algorithms output positive-definite matrices, correspond to existing techniques in linear regression literature. Specifically, we discuss the following three techniques. (i) For Ridge Regression, we propose setting the regularization coefficient so that by approximating the solution using Johnson-Lindenstrauss transform we preserve privacy. (ii) We show that adding a small batch of random samples to our data preserves differential privacy. (iii) We show that sampling the 2nd-moment matrix from a Bayesian posterior inverse-Wishart distribution is differentially private provided the prior is set correctly. We also evaluate our techniques experimentally and compare them to the existing "Analyze Gauss" algorithm of Dwork et al.

cs.DS↗

arXiv2014

Learning Mixtures of Ranking Models

This work concerns learning probabilistic models for ranking data in a heterogeneous population. The specific problem we study is learning the parameters of a Mallows Mixture Model. Despite being widely studied, current heuristics for this problem do not have theoretical guarantees and can get stuck in bad local optima. We present the first polynomial time algorithm which provably learns the parameters of a mixture of two Mallows models. A key component of our algorithm is a novel use of tensor decomposition techniques to learn the top-k prefix in both the rankings. Before this work, even the question of identifiability in the case of a mixture of two Mallows models was unresolved.

cs.LG↗

arXiv2014

Privacy Games

The problem of analyzing the effect of privacy concerns on the behavior of selfish utility-maximizing agents has received much attention lately. Privacy concerns are often modeled by altering the utility functions of agents to consider also their privacy loss. Such privacy aware agents prefer to take a randomized strategy even in very simple games in which non-privacy aware agents play pure strategies. In some cases, the behavior of privacy aware agents follows the framework of Randomized Response, a well-known mechanism that preserves differential privacy. Our work is aimed at better understanding the behavior of agents in settings where their privacy concerns are explicitly given. We consider a toy setting where agent A, in an attempt to discover the secret type of agent B, offers B a gift that one type of B agent likes and the other type dislikes. As opposed to previous works, B's incentive to keep her type a secret isn't the result of "hardwiring" B's utility function to consider privacy, but rather takes the form of a payment between B and A. We investigate three different types of payment functions and analyze B's behavior in each of the resulting games. As we show, under some payments, B's behavior is very different than the behavior of agents with hardwired privacy concerns and might even be deterministic. Under a different payment we show that B's BNE strategy does fall into the framework of Randomized Response.

cs.GT↗

arXiv2013

Optimizing Password Composition Policies

A password composition policy restricts the space of allowable passwords to eliminate weak passwords that are vulnerable to statistical guessing attacks. Usability studies have demonstrated that existing password composition policies can sometimes result in weaker password distributions; hence a more principled approach is needed. We introduce the first theoretical model for optimizing password composition policies. We study the computational and sample complexity of this problem under different assumptions on the structure of policies and on users' preferences over passwords. Our main positive result is an algorithm that -- with high probability --- constructs almost optimal policies (which are specified as a union of subsets of allowed passwords), and requires only a small number of samples of users' preferred passwords. We complement our theoretical results with simulations using a real-world dataset of 32 million passwords.

cs.CR↗