Related papers: New Lower Bounds for Private Estimation and a Gene…
We present novel, computationally efficient, and differentially private algorithms for two fundamental high-dimensional learning problems: learning a multivariate Gaussian and learning a product distribution over the Boolean hypercube in…
Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent this problem is to assume that the covariance matrix is…
We revisit the problem of releasing the sample mean of bounded samples in a dataset, privately, under user-level $\varepsilon$-differential privacy (DP). We aim to derive the optimal method of preprocessing data samples, within a canonical…
In this paper, we revisit the problem of sparse linear regression in the local differential privacy (LDP) model. Existing research in the non-interactive and sequentially local models has focused on obtaining the lower bounds for the case…
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…
Recent years, local differential privacy (LDP) has been adopted by many web service providers like Google \cite{erlingsson2014rappor}, Apple \cite{apple2017privacy} and Microsoft \cite{bolin2017telemetry} to collect and analyse users' data…
Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this…
We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we…
We develop a sharp, experiment-level privacy theory for amplification by shuffling in the Gaussian regime: a fixed finite-output local randomizer with full support and neighboring binary datasets differing in one user. We first prove exact…
In recent years, Gaussian noise has become a popular tool in differentially private algorithms, often replacing Laplace noise which dominated the early literature. Gaussian noise is the standard approach to $\textit{approximate}$…
Differentially Private Stochastic Gradient Descent (DP-SGD) is the dominant paradigm for private training, but its fundamental limitations under worst-case adversarial privacy definitions remain poorly understood. We analyze DP-SGD in the…
We characterize the minimum noise amplitude and power for noise-adding mechanisms in $(\epsilon, \delta)$-differential privacy for single real-valued query function. We derive new lower bounds using the duality of linear programming, and…
The Horvitz-Thompson estimate of a total can be seen as as differentially private mechanism applied to this population total. We provide forumlae to compute the $\epsilon$ and $\delta$ parameter for this specific mecanism, coupled or not…
In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower…
We introduce a novel framework for differentially private (DP) statistical estimation via data truncation, addressing a key challenge in DP estimation when the data support is unbounded. Traditional approaches rely on problem-specific…
In recent years, differential privacy has been adopted by tech-companies and governmental agencies as the standard for measuring privacy in algorithms. In this article, we study differential privacy in Bayesian posterior sampling settings.…
Deep heteroscedastic regression models the mean and covariance of the target distribution through neural networks. The challenge arises from heteroscedasticity, which implies that the covariance is sample dependent and is often unknown.…
The last few years have seen a surge of work on high dimensional statistics under privacy constraints, mostly following two main lines of work: the ``worst case'' line, which does not make any distributional assumptions on the input data;…
This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…
A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…