Related papers: A Unifying Framework for Differentially Private Su…
In this paper, we investigate the differentially private estimation of data depth functions and their associated medians. We introduce several methods for privatizing depth values at a fixed point, and show that for some depth functions,…
We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…
Computing the core decomposition of a graph is a fundamental problem that has recently been studied in the differentially private setting, motivated by practical applications in data mining. In particular, Dhulipala et al. [FOCS 2022] gave…
We use the Sum of Squares method to develop new efficient algorithms for learning well-separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that substantially improve upon the statistical guarantees achieved…
Estimating the quantiles of a large dataset is a fundamental problem in both the streaming algorithms literature and the differential privacy literature. However, all existing private mechanisms for distribution-independent quantile…
We study differentially-private statistics in the fully dynamic continual observation model, where many updates can arrive at each time step and updates to a stream can involve both insertions and deletions of an item. Earlier work (e.g.,…
Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental…
We give new dequantization and hardness results for estimating spectral sums of matrices, such as the log-determinant. Recent quantum algorithms have demonstrated that the logarithm of the determinant of sparse, well-conditioned, positive…
With the growing volume of data in society, the need for privacy protection in data analysis also rises. In particular, private selection tasks, wherein the most important information is retrieved under differential privacy are emphasized…
The classical persistence algorithm computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological…
Training machine learning models with differential privacy (DP) has received increasing interest in recent years. One of the most popular algorithms for training differentially private models is differentially private stochastic gradient…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
We study the convergence rate of the proximal-gradient homotopy algorithm applied to norm-regularized linear least squares problems, for a general class of norms. The homotopy algorithm reduces the regularization parameter in a series of…
There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of…
We study private matrix analysis in the sliding window model where only the last $W$ updates to matrices are considered useful for analysis. We give first efficient $o(W)$ space differentially private algorithms for spectral approximation,…
Soft extrapolation refers to the problem of recovering a function from its samples, multiplied by a fast-decaying window and perturbed by an additive noise, over an interval which is potentially larger than the essential support of the…
We analyze the performance of the greedy algorithm, and also a discrete semi-gradient based algorithm, for maximizing the sum of a suBmodular and suPermodular (BP) function (both of which are non-negative monotone non-decreasing) under two…
We introduce efficient differentially private (DP) algorithms for several linear algebraic tasks, including solving linear equalities over arbitrary fields, linear inequalities over the reals, and computing affine spans and convex hulls. As…
We present a novel sequential Monte Carlo approach to online smoothing of additive functionals in a very general class of path-space models. Hitherto, the solutions proposed in the literature suffer from either long-term numerical…
We initiate a systematic study of algorithms that are both differentially private and run in sublinear time for several problems in which the goal is to estimate natural graph parameters. Our main result is a differentially-private…