Related papers: Better and Simpler Lower Bounds for Differentially…

Differential privacy changes the effective sample size governing CVaR learning. For tail mass $\tau$, the privacy-relevant sample size is not $n$, but $n\tau$; equivalently, the effective private tail sample size is $\epsilon n\tau$.…

In this work, we study high-dimensional mean estimation under user-level differential privacy, and design an $(\varepsilon,\delta)$-differentially private mechanism using as few users as possible. In particular, we provide a nearly optimal…

We study the algorithmic problem of estimating the mean of heavy-tailed random vector in $\mathbb{R}^d$, given $n$ i.i.d. samples. The goal is to design an efficient estimator that attains the optimal sub-gaussian error bound, only assuming…

We describe Bayesian inference for the parameters of Gaussian models of bounded data protected by differential privacy. Using this setting, we demonstrate that analysts can and should take constraints imposed by the bounds into account when…

We study the canonical statistical task of computing the principal component from $n$ i.i.d.~data in $d$ dimensions under $(\varepsilon,\delta)$-differential privacy. Although extensively studied in literature, existing solutions fall short…

We give the first polynomial-time, polynomial-sample, differentially private estimator for the mean and covariance of an arbitrary Gaussian distribution $\mathcal{N}(\mu,\Sigma)$ in $\mathbb{R}^d$. All previous estimators are either…

The Gaussian mechanism is one differential privacy mechanism commonly used to protect numerical data. However, it may be ill-suited to some applications because it has unbounded support and thus can produce invalid numerical answers to…

We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector $X$ has finite mean and covariance. In this setting, the radius of confidence intervals achieved…

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…

We revisit the problem of robust linear regression under Gaussian covariates with an unknown covariance matrix of condition number $\kappa$. For this fundamental problem, significant gaps remain in our understanding of the trade-offs among…

Although there is an extensive literature on the maxima of Gaussian processes, there are relatively few non-asymptotic bounds on their lower-tail probabilities. The aim of this paper is to develop such a bound, while also allowing for many…

Differential privacy is a cryptographically-motivated definition of privacy which has gained significant attention over the past few years. Differentially private solutions enforce privacy by adding random noise to a function computed over…

We consider the problem of learning mixtures of Gaussians under the constraint of approximate differential privacy. We prove that $\widetilde{O}(k^2 d \log^{3/2}(1/\delta) / \alpha^2 \varepsilon)$ samples are sufficient to learn a mixture…

The Gaussian distribution is widely used in mechanism design for differential privacy (DP). Thanks to its sub-Gaussian tail, it significantly reduces the chance of outliers when responding to queries. However, it can only provide…

Stochastic convex optimization over an $\ell_1$-bounded domain is ubiquitous in machine learning applications such as LASSO but remains poorly understood when learning with differential privacy. We show that, up to logarithmic factors the…

The most effective differentially private machine learning algorithms in practice rely on an additional source of purportedly public data. This paradigm is most interesting when the two sources combine to be more than the sum of their…

We study the problem of differentially private stochastic convex optimization (DP-SCO) with heavy-tailed gradients, where we assume a $k^{\text{th}}$-moment bound on the Lipschitz constants of sample functions rather than a uniform bound.…

We study the problem of fitting the high dimensional sparse linear regression model with sub-Gaussian covariates and responses, where the data are provided by strategic or self-interested agents (individuals) who prioritize their privacy of…

We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…

We present a fairly general framework for reducing $(\varepsilon, \delta)$ differentially private (DP) statistical estimation to its non-private counterpart. As the main application of this framework, we give a polynomial time and…