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We consider the problem of privately estimating a parameter $\mathbb{E}[h(X_1,\dots,X_k)]$, where $X_1$, $X_2$, $\dots$, $X_k$ are i.i.d. data from some distribution and $h$ is a permutation-invariant function. Without privacy constraints,…

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…

We study instrumental variable regression (IVaR) under differential privacy constraints. Classical IVaR methods (like two-stage least squares regression) rely on solving moment equations that directly use sensitive covariates and…

The wide deployment of machine learning in recent years gives rise to a great demand for large-scale and high-dimensional data, for which the privacy raises serious concern. Differential privacy (DP) mechanisms are conventionally developed…

A key tool for building differentially private systems is adding Gaussian noise to the output of a function evaluated on a sensitive dataset. Unfortunately, using a continuous distribution presents several practical challenges. First and…

Computing matchings in graphs is a foundational algorithmic task. Despite extensive interest in differentially private (DP) graph analysis, work on privately computing matching solutions, rather than just their size, has been sparse. The…

We prove a \emph{query complexity} lower bound on rank-one principal component analysis (PCA). We consider an oracle model where, given a symmetric matrix $M \in \mathbb{R}^{d \times d}$, an algorithm is allowed to make $T$ \emph{exact}…

Differential Privacy (DP) is the current gold-standard for ensuring privacy for statistical queries. Estimation problems under DP constraints appearing in the literature have largely focused on providing equal privacy to all users. We…

Many commonly used learning algorithms work by iteratively updating an intermediate solution using one or a few data points in each iteration. Analysis of differential privacy for such algorithms often involves ensuring privacy of each step…

We show that convex-concave Lipschitz stochastic saddle point problems (also known as stochastic minimax optimization) can be solved under the constraint of $(\epsilon,\delta)$-differential privacy with \emph{strong (primal-dual) gap} rate…

Gaussian processes (GPs) are non-parametric Bayesian models that are widely used for diverse prediction tasks. Previous work in adding strong privacy protection to GPs via differential privacy (DP) has been limited to protecting only the…

This paper addresses the problem of differentially private distributed optimization under limited communication, where each agent aims to keep their cost function private while minimizing the sum of all agents' cost functions. In response,…

In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations…

We prove a \emph{query complexity} lower bound for approximating the top $r$ dimensional eigenspace of a matrix. We consider an oracle model where, given a symmetric matrix $\mathbf{M} \in \mathbb{R}^{d \times d}$, an algorithm…

In this paper we present an extremely general method for approximately solving a large family of convex programs where the solution can be divided between different agents, subject to joint differential privacy. This class includes…

The widespread proliferation of data-driven decision-making has ushered in a recent interest in the design of privacy-preserving algorithms. In this paper, we consider the ubiquitous problem of gaussian process (GP) bandit optimization from…

Sparse PCA is the optimization problem obtained from PCA by adding a sparsity constraint on the principal components. Sparse PCA is NP-hard and hard to approximate even in the single-component case. In this paper we settle the computational…

Prior work on differential privacy analysis of randomized SGD algorithms relies on composition theorems, where the implicit (unrealistic) assumption is that the internal state of the iterative algorithm is revealed to the adversary. As a…

We propose a numerical accountant for evaluating the tight $(\varepsilon,\delta)$-privacy loss for algorithms with discrete one dimensional output. The method is based on the privacy loss distribution formalism and it uses the recently…

A basic problem in the design of privacy-preserving algorithms is the private maximization problem: the goal is to pick an item from a universe that (approximately) maximizes a data-dependent function, all under the constraint of…