Related papers: On Differentially Private Linear Algebra
In this paper, we initiate the systematic study of solving linear programs under differential privacy. The first step is simply to define the problem: to this end, we introduce several natural classes of private linear programs that capture…
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…
We present differentially private (DP) algorithms for bilevel optimization, a problem class that received significant attention lately in various machine learning applications. These are the first algorithms for such problems under standard…
Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with…
Numerical linear algebra plays an important role in computer science. In this paper, we initiate the study of performing linear algebraic tasks while preserving privacy when the data is streamed online. Our main focus is the space…
We present differentially private efficient algorithms for learning union of polygons in the plane (which are not necessarily convex). Our algorithms achieve $(\alpha,\beta)$-PAC learning and $(\epsilon,\delta)$-differential privacy using a…
Developing a differentially private deep learning algorithm is challenging, due to the difficulty in analyzing the sensitivity of objective functions that are typically used to train deep neural networks. Many existing methods resort to the…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
We give new differentially private algorithms for the classic problems of learning decision lists and large-margin halfspaces in the PAC and online models. In the PAC model, we give a computationally efficient algorithm for learning…
We study the problem of solving linear programs of the form $Ax\le b$, $x\ge0$ with differential privacy. For homogeneous LPs $Ax\ge0$, we give an efficient $(\epsilon,\delta)$-differentially private algorithm which with probability at…
We present a differentially private learner for halfspaces over a finite grid $G$ in $\mathbb{R}^d$ with sample complexity $\approx d^{2.5}\cdot 2^{\log^*|G|}$, which improves the state-of-the-art result of [Beimel et al., COLT 2019] by a…
We study differentially private approximation algorithms for positive linear programs (LPs with nonnegative coefficients and variables), focusing on the fundamental families of packing, covering, and mixed packing-covering formulations. We…
Private data analysis suffers a costly curse of dimensionality. However, the data often has an underlying low-dimensional structure. For example, when optimizing via gradient descent, the gradients often lie in or near a low-dimensional…
This study examines a resource-sharing problem involving multiple parties that agree to use a set of capacities together. We start with modeling the whole problem as a mathematical program, where all parties are required to exchange…
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…
In this paper, we study differentially private (DP) algorithms for computing the geometric median (GM) of a dataset: Given $n$ points, $x_1,\dots,x_n$ in $\mathbb{R}^d$, the goal is to find a point $\theta$ that minimizes the sum of the…
We introduce new differentially private (DP) mechanisms for gradient-based machine learning (ML) with multiple passes (epochs) over a dataset, substantially improving the achievable privacy-utility-computation tradeoffs. We formalize the…
Recently, several striking advances have taken place regarding the discrete logarithm problem (DLP) in finite fields of small characteristic, despite progress having remained essentially static for nearly thirty years, with the best known…
Machine learning with formal privacy-preserving techniques like Differential Privacy (DP) allows one to derive valuable insights from sensitive medical imaging data while promising to protect patient privacy, but it usually comes at a sharp…
Linear programming is a fundamental tool in a wide range of decision systems. However, without privacy protections, sharing the solution to a linear program may reveal information about the underlying data used to formulate it, which may be…