Related papers: Lower Bounds for Locally Private Estimation via Co…
The minimum mean-square error (MMSE) achievable by optimal estimation of a random variable $Y\in\mathbb{R}$ given another random variable $X\in\mathbb{R}^{d}$ is of much interest in a variety of statistical settings. In the context of…
A continuing challenge for machine learning is providing methods to perform computation on data while ensuring the data remains private. In this paper we build on the provable privacy guarantees of differential privacy which has been…
The notion of $\varepsilon$-differential privacy is a widely used concept of providing quantifiable privacy to individuals. However, it is unclear how to explain the level of privacy protection provided by a differential privacy mechanism…
We present two sample-efficient differentially private mean estimators for $d$-dimensional (sub)Gaussian distributions with unknown covariance. Informally, given $n \gtrsim d/\alpha^2$ samples from such a distribution with mean $\mu$ and…
We study the sample complexity of learning threshold functions under the constraint of differential privacy. It is assumed that each labeled example in the training data is the information of one individual and we would like to come up with…
Previous studies yielded discouraging results for item-level locally differentially private linear regression with $s^*$-sparsity assumption, where the minimax rate for $nm$ samples is $\mathcal{O}(s^{*}d / nm\varepsilon^2)$. This can be…
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 consider the minimax estimation problem of a discrete distribution with support size $k$ under locally differential privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the…
In this paper, we investigate one of the most fundamental nonconvex learning problems, ReLU regression, in the Differential Privacy (DP) model. Previous studies on private ReLU regression heavily rely on stringent assumptions, such as…
Based on binary inquiries, we developed an algorithm to estimate population quantiles under Local Differential Privacy (LDP). By self-normalizing, our algorithm provides asymptotically normal estimation with valid inference, resulting in…
Adding random noise to database query results is an important tool for achieving privacy. A challenge is to minimize this noise while still meeting privacy requirements. Recently, a sufficient and necessary condition for $(\epsilon,…
Recent research in differential privacy demonstrated that (sub)sampling can amplify the level of protection. For example, for $\epsilon$-differential privacy and simple random sampling with sampling rate $r$, the actual privacy guarantee is…
This work shows how to privately and more accurately estimate Euclidean distance between pairs of vectors. Input vectors $x$ and $y$ are mapped to differentially private sketches $x'$ and $y'$, from which one can estimate the distance…
We prove new upper and lower bounds on the sample complexity of $(\epsilon, \delta)$ differentially private algorithms for releasing approximate answers to threshold functions. A threshold function $c_x$ over a totally ordered domain $X$…
Differentially Private Stochastic Gradient Descent (DPSGD) is widely used to protect sensitive data during the training of machine learning models, but its privacy guarantee often comes at a large cost of model performance due to the lack…
In the era of big data, it is necessary to split extremely large data sets across multiple computing nodes and construct estimators using the distributed data. When designing distributed estimators, it is desirable to minimize the amount of…
The standard closed form lower bound on $\sigma$ for providing $(\epsilon, \delta)$-differential privacy by adding zero mean Gaussian noise with variance $\sigma^2$ is $\sigma > \Delta\sqrt {2}(\epsilon^{-1}) \sqrt {\log \left(…
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…
Motivated by the rapid rise in statistical tools in Functional Data Analysis, we consider the Gaussian mechanism for achieving differential privacy with parameter estimates taking values in a, potentially infinite-dimensional, separable…
We consider the problem of estimating a regression function from anonymized data in the framework of local differential privacy. We propose a novel partitioning estimate of the regression function, derive a rate of convergence for the…