相关论文: Asymptotically optimal private estimation under me…

We study the statistical complexity of private linear regression under an unknown, potentially ill-conditioned covariate distribution. Somewhat surprisingly, under privacy constraints the intrinsic complexity is \emph{not} captured by the…

We analyze statistical features of the ``optimization landscape'' in a random version of one of the simplest constrained optimization problems of the least-square type: finding the best approximation for the solution of an overcomplete…

We consider non-parametric density estimation in the framework of local approximate differential privacy. In contrast to centralized privacy scenarios with a trusted curator, in the local setup anonymization must be guaranteed already on…

We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…

Differential Privacy (DP) is a well-established framework to quantify privacy loss incurred by any algorithm. Traditional DP formulations impose a uniform privacy requirement for all users, which is often inconsistent with real-world…

A deterministic privacy metric using non-stochastic information theory is developed. Particularly, minimax information is used to construct a measure of information leakage, which is inversely proportional to the measure of privacy. Anyone…

One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and…

We study the problem of setting a price for a potential buyer with a valuation drawn from an unknown distribution $D$. The seller has "data"' about $D$ in the form of $m \ge 1$ i.i.d. samples, and the algorithmic challenge is to use these…

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…

Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with…

This work studies the distributed empirical risk minimization (ERM) problem under differential privacy (DP) constraint. Standard distributed algorithms achieve DP typically by perturbing all local subgradients with noise, leading to…

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…

We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…

In this paper, we focus our attention on private Empirical Risk Minimization (ERM), which is one of the most commonly used data analysis method. We take the first step towards solving the above problem by theoretically exploring the effect…

We study the canonical statistical estimation problem of linear regression from $n$ i.i.d.~examples under $(\varepsilon,\delta)$-differential privacy when some response variables are adversarially corrupted. We propose a variant of the…

We study predictive density estimation under Kullback-Leibler loss in $\ell_0$-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. A surprise is the…

The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that…

We study the minimax estimation of $\alpha$-divergences between discrete distributions for integer $\alpha\ge 1$, which include the Kullback--Leibler divergence and the $\chi^2$-divergences as special examples. Dropping the usual…

We develop two notions of instance optimality in differential privacy, inspired by classical statistical theory: one by defining a local minimax risk and the other by considering unbiased mechanisms and analogizing the Cramer-Rao bound, and…

We study statistical risk minimization problems under a privacy model in which the data is kept confidential even from the learner. In this local privacy framework, we establish sharp upper and lower bounds on the convergence rates of…