Related papers: Tight Differentially Private PCA via Matrix Cohere…

We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time…

We study spectral graph clustering under edge differential privacy. We propose a matrix shuffling mechanism that combines randomized edge flipping with a random permutation of the adjacency matrix. While edge flipping alone provides only a…

In differential privacy, random noise is introduced to privatize summary statistics of a sensitive dataset before releasing them. The noise level determines the privacy loss, which quantifies how easily an adversary can detect a target…

A major challenge for machine learning is increasing the availability of data while respecting the privacy of individuals. Here we combine the provable privacy guarantees of the differential privacy framework with the flexibility of…

Differential privacy via output perturbation has been a de facto standard for releasing query or computation results on sensitive data. However, we identify that all existing Gaussian mechanisms suffer from the curse of full-rank covariance…

We study the problem of differentially private optimization with linear constraints when the right-hand-side of the constraints depends on private data. This type of problem appears in many applications, especially resource allocation.…

We study the classical problem of community recovery in stochastic block models with a fixed number of communities, with a twist: We seek algorithms that are stable with respect to node-wise changes in the graph structure, formally defined…

We consider the task of privately obtaining prediction error guarantees in ordinary least-squares regression problems with Gaussian covariates (with unknown covariance structure). We provide the first sample-optimal polynomial time…

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal…

This paper proposes a differentially private recursive least squares algorithm to estimate the parameter of autoregressive systems with exogenous inputs and multi-participants (MP-ARX systems) and protect each participant's sensitive…

We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish lower bounds on the rates of convergence of the estimators of the…

We develop two methods for the following fundamental statistical task: given an $\epsilon$-corrupted set of $n$ samples from a $d$-dimensional sub-Gaussian distribution, return an approximate top eigenvector of the covariance matrix. Our…

Differential privacy is the leading mathematical framework for privacy protection, providing a probabilistic guarantee that safeguards individuals' private information when publishing statistics from a dataset. This guarantee is achieved by…

Ensuring differential privacy of models learned from sensitive user data is an important goal that has been studied extensively in recent years. It is now known that for some basic learning problems, especially those involving…

Auditing mechanisms for differential privacy use probabilistic means to empirically estimate the privacy level of an algorithm. For private machine learning, existing auditing mechanisms are tight: the empirical privacy estimate (nearly)…

We introduce the (Wishart) projection mechanism, a randomized map of the form $S \mapsto M f(S)$ with $M \sim W_d(1/r I_d, r)$ and study its differential privacy properties. For vector-valued queries $f$, we prove non-asymptotic DP…

We design new differentially private algorithms for the Euclidean k-means problem, both in the centralized model and in the local model of differential privacy. In both models, our algorithms achieve significantly improved error guarantees…

Differentially private (DP) machine learning has recently become popular. The privacy loss of DP algorithms is commonly reported using $(\varepsilon,\delta)$-DP. In this paper, we propose a numerical accountant for evaluating the privacy…

We develop theoretically guaranteed stochastic methods for outlier-robust PCA. Outlier-robust PCA seeks an underlying low-dimensional linear subspace from a dataset that is corrupted with outliers. We are able to show that our methods,…