Related papers: Asymptotically optimal private estimation under me…
Standard techniques for differentially private estimation, such as Laplace or Gaussian noise addition, require guaranteed bounds on the sensitivity of the estimator in question. But such sensitivity bounds are often large or simply unknown.…
Numerical vector aggregation plays a crucial role in privacy-sensitive applications, such as distributed gradient estimation in federated learning and statistical analysis of key-value data. In the context of local differential privacy,…
We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide…
We explore the trade-off between privacy and statistical utility in private two-sample testing under local differential privacy (LDP) for both multinomial and continuous data. We begin by addressing the multinomial case, where we introduce…
We consider a data analyst's problem of purchasing data from strategic agents to compute an unbiased estimate of a statistic of interest. Agents incur private costs to reveal their data and the costs can be arbitrarily correlated with their…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
Fine-tuning adapts a pretrained machine learning model to a small, sensitive dataset, but this process risks memorizing individual new data points, making the model vulnerable to adversaries who seek to extract sensitive information. In…
This work provides tight upper- and lower-bounds for the problem of mean estimation under $\epsilon$-differential privacy in the local model, when the input is composed of $n$ i.i.d. drawn samples from a normal distribution with variance…
Consider a central problem in randomized approximation schemes that use a Monte Carlo approach. Given a sequence of independent, identically distributed random variables $X_1,X_2,\ldots$ with mean $\mu$ and standard deviation at most $c…
Estimating optimal transport maps between two distributions from respective samples is an important element for many machine learning methods. To do so, rather than extending discrete transport maps, it has been shown that estimating the…
We initiate an investigation of private sampling from distributions. Given a dataset with $n$ independent observations from an unknown distribution $P$, a sampling algorithm must output a single observation from a distribution that is close…
We revisit the problem of linear regression under a differential privacy constraint. By consolidating existing pieces in the literature, we clarify the correct dependence of the feature, label and coefficient domains in the optimization…
Differentially private computation often begins with a bound on some $d$-dimensional statistic's $\ell_p$ sensitivity. For pure differential privacy, the $K$-norm mechanism can improve on this approach using a norm tailored to the…
Many algorithms have been developed to estimate probability distributions subject to differential privacy (DP): such an algorithm takes as input independent samples from a distribution and estimates the density function in a way that is…
We consider the problem of collaborative personalized mean estimation under a privacy constraint in an environment of several agents continuously receiving data according to arbitrary unknown agent-specific distributions. In particular, we…
Devising mechanisms with good beyond-worst-case input-dependent performance has been an important focus of differential privacy, with techniques such as smooth sensitivity, propose-test-release, or inverse sensitivity mechanism being…
For scalable machine learning on large data sets, subsampling a representative subset is a common approach for efficient model training. This is often achieved through importance sampling, whereby informative data points are sampled more…
Networked system often relies on distributed algorithms to achieve a global computation goal with iterative local information exchanges between neighbor nodes. To preserve data privacy, a node may add a random noise to its original data for…
We consider the problem of estimating the $L_1$ distance between two discrete probability measures $P$ and $Q$ from empirical data in a nonasymptotic and large alphabet setting. When $Q$ is known and one obtains $n$ samples from $P$, we…
We develop a privacy-preserving distributed projection least mean squares (LMS) strategy over linear multitask networks, where agents' local parameters of interest or tasks are linearly related. Each agent is interested in not only…