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We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
Estimating the quantiles of a large dataset is a fundamental problem in both the streaming algorithms literature and the differential privacy literature. However, all existing private mechanisms for distribution-independent quantile…
We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic…
We give the first polynomial-time, polynomial-sample, differentially private estimator for the mean and covariance of an arbitrary Gaussian distribution $\mathcal{N}(\mu,\Sigma)$ in $\mathbb{R}^d$. All previous estimators are either…
We study efficient differentially private algorithms for estimating monotone statistics, i.e., statistics that are monotone under the addition of new observations. The starting point for our investigation is subsample-and-aggregate: a…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
The simplest and most widely applied method for guaranteeing differential privacy is to add instance-independent noise to a statistic of interest that is scaled to its global sensitivity. However, global sensitivity is a worst-case notion…
Differentially Private algorithms often need to select the best amongst many candidate options. Classical works on this selection problem require that the candidates' goodness, measured as a real-valued score function, does not change by…
We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially…
Measuring the stability of conclusions derived from Ordinary Least Squares linear regression is critically important, but most metrics either only measure local stability (i.e. against infinitesimal changes in the data), or are only…
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…
We propose a rate optimal estimator for the linear regression model on network data with interacted (unobservable) individual effects. The estimator achieves a faster rate of convergence $N$ compared to the standard estimators' $\sqrt{N}$…
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 linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
Datasets are often reused to perform multiple statistical analyses in an adaptive way, in which each analysis may depend on the outcomes of previous analyses on the same dataset. Standard statistical guarantees do not account for 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…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
As the scale of problems and data used for experimental design, signal processing and data assimilation grow, the oft-occuring least squares subproblems are correspondingly growing in size. As the scale of these least squares problems…
In this paper, we study the distributed adaptive estimation problem of continuous-time stochastic dynamic systems over sensor networks where each agent can only communicate with its local neighbors. A distributed least squares (LS)…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…