Related papers: Insufficient Statistics Perturbation: Stable Estim…
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…
This paper proposes a new distributed nonconvex stochastic optimization algorithm that can achieve privacy protection, communication efficiency and convergence simultaneously. Specifically, each node adds general privacy noises to its local…
We study differentially private (DP) optimization algorithms for stochastic and empirical objectives which are neither smooth nor convex, and propose methods that return a Goldstein-stationary point with sample complexity bounds that…
We develop differentially private methods for estimating various distributional properties. Given a sample from a discrete distribution $p$, some functional $f$, and accuracy and privacy parameters $\alpha$ and $\varepsilon$, the goal is to…
This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of It\^o drift…
We study differentially private (DP) algorithms for smooth stochastic minimax optimization, with stochastic minimization as a byproduct. The holy grail of these settings is to guarantee the optimal trade-off between the privacy and the…
This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause…
We consider linear time invariant systems with exogenous stochastic disturbances, and in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. Our concern is…
In non-private stochastic convex optimization, stochastic gradient methods converge much faster on interpolation problems -- problems where there exists a solution that simultaneously minimizes all of the sample losses -- than on…
We propose a new definition of instance optimality for differentially private estimation algorithms. Our definition requires an optimal algorithm to compete, simultaneously for every dataset $D$, with the best private benchmark algorithm…
Decentralized algorithms for stochastic optimization and learning rely on the diffusion of information as a result of repeated local exchanges of intermediate estimates. Such structures are particularly appealing in situations where agents…
For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…
This paper presents a simple yet efficient method for statistical inference of tensor linear forms using incomplete and noisy observations. Under the Tucker low-rank tensor model and the missing-at-random assumption, we utilize an…
Ratio statistics--such as relative risk and odds ratios--play a central role in hypothesis testing, model evaluation, and decision-making across many areas of machine learning, including causal inference and fairness analysis. However,…
Local differential privacy is a differential privacy paradigm in which individuals first apply a privacy mechanism to their data (often by adding noise) before transmitting the result to a curator. The noise for privacy results in…
We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in…
We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified…
We study differentially private stochastic optimization in convex and non-convex settings. For the convex case, we focus on the family of non-smooth generalized linear losses (GLLs). Our algorithm for the $\ell_2$ setting achieves optimal…
This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain…
We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…