Related papers: Differentially Private Medians and Interior Points…
We design an $(\varepsilon, \delta)$-differentially private algorithm to estimate the mean of a $d$-variate distribution, with unknown covariance $\Sigma$, that is adaptive to $\Sigma$. To within polylogarithmic factors, the estimator…
This study presents new closed-form estimators for the Dirichlet and the Multivariate Gamma distribution families, whose maximum likelihood estimator cannot be explicitly derived. The methodology builds upon the score-adjusted estimators…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
In this work, we propose estimators for the uncertainty in mean residual times that require, for their evaluation, statistically independent individual residence times obtained from a discrete time process. We examine their performance…
Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…
We develop plug-in estimators for locally differentially private semi-parametric estimation via spline wavelets. The approach leads to optimal rates of convergence for a large class of estimation problems that are characterized by…
We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
We study the problem of learning exponential distributions under differential privacy. Given $n$ i.i.d.\ samples from $\mathrm{Exp}(\lambda)$, the goal is to privately estimate $\lambda$ so that the learned distribution is close in total…
We consider the problem of constructing confidence intervals for the median of a response $Y \in \mathbb{R}$ conditional on features $X \in \mathbb{R}^d$ in a situation where we are not willing to make any assumption whatsoever on the…
We explore the power of the hybrid model of differential privacy (DP), in which some users desire the guarantees of the local model of DP and others are content with receiving the trusted-curator model guarantees. In particular, we study…
We establish a general framework for statistical inferences with non-probability survey samples when relevant auxiliary information is available from a probability survey sample. We develop a rigorous procedure for estimating the propensity…
We introduce a novel framework for differentially private (DP) statistical estimation via data truncation, addressing a key challenge in DP estimation when the data support is unbounded. Traditional approaches rely on problem-specific…
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class…
Private data analysis suffers a costly curse of dimensionality. However, the data often has an underlying low-dimensional structure. For example, when optimizing via gradient descent, the gradients often lie in or near a low-dimensional…
We present a private learner for halfspaces over an arbitrary finite domain $X\subset \mathbb{R}^d$ with sample complexity $mathrm{poly}(d,2^{\log^*|X|})$. The building block for this learner is a differentially private algorithm for…
Maximum pseudolikelihood (MPL) estimators are useful alternatives to maximum likelihood (ML) estimators when likelihood functions are more difficult to manipulate than their marginal and conditional components. Furthermore, MPL estimators…
We study the fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over $k$ elements, under differential privacy. While the problems have a long history in statistics, finite…
Estimating mutual information between continuous random variables is often intractable and extremely challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
Differential privacy formalises privacy-preserving mechanisms that provide access to a database. We pose the question of whether Bayesian inference itself can be used directly to provide private access to data, with no modification. The…