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Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between…
We consider the task of privately obtaining prediction error guarantees in ordinary least-squares regression problems with Gaussian covariates (with unknown covariance structure). We provide the first sample-optimal polynomial time…
A wide variety of fundamental data analyses in machine learning, such as linear and logistic regression, require minimizing a convex function defined by the data. Since the data may contain sensitive information about individuals, and these…
We provide computationally efficient, differentially private algorithms for the classical regression settings of Least Squares Fitting, Binary Regression and Linear Regression with unbounded covariates. Prior to our work, privacy…
We provide a detailed study of the estimation of probability distributions---discrete and continuous---in a stringent setting in which data is kept private even from the statistician. We give sharp minimax rates of convergence for…
Although robust learning and local differential privacy are both widely studied fields of research, combining the two settings is just starting to be explored. We consider the problem of estimating a discrete distribution in total variation…
Economics and social science research often require analyzing datasets of sensitive personal information at fine granularity, with models fit to small subsets of the data. Unfortunately, such fine-grained analysis can easily reveal…
Linear regression is an important tool across many fields that work with sensitive human-sourced data. Significant prior work has focused on producing differentially private point estimates, which provide a privacy guarantee to individuals…
We study the problem of differentially private optimization with linear constraints when the right-hand-side of the constraints depends on private data. This type of problem appears in many applications, especially resource allocation.…
Convex programming with linear constraints plays an important role in the operation of a number of everyday systems. However, absent any additional protections, revealing or acting on the solutions to such problems may reveal information…
Contextual bandit with linear reward functions is among one of the most extensively studied models in bandit and online learning research. Recently, there has been increasing interest in designing \emph{locally private} linear contextual…
We consider the problem of fitting a linear model to data held by individuals who are concerned about their privacy. Incentivizing most players to truthfully report their data to the analyst constrains our design to mechanisms that provide…
A recently proposed scheme utilizing local noise addition and matrix masking enables data collection while protecting individual privacy from all parties, including the central data manager. Statistical analysis of such privacy-preserved…
We propose differentially private algorithms for parameter estimation in both low-dimensional and high-dimensional sparse generalized linear models (GLMs) by constructing private versions of projected gradient descent. We show that the…
Privacy preservation has become a critical concern in high-dimensional data analysis due to the growing prevalence of data-driven applications. Since its proposal, sliced inverse regression has emerged as a widely utilized statistical…
Linear regression is frequently applied in a variety of domains, some of which might contain sensitive information. This necessitates that the application of these methods does not reveal private information. Differentially private (DP)…
There has been increasing demand for establishing privacy-preserving methodologies for modern statistics and machine learning. Differential privacy, a mathematical notion from computer science, is a rising tool offering robust privacy…
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…
We identify fundamental tradeoffs between statistical utility and privacy under local models of privacy in which data is kept private even from the statistician, providing instance-specific bounds for private estimation and learning…
Existing work on differentially private linear regression typically assumes that end users can precisely set data bounds or algorithmic hyperparameters. End users often struggle to meet these requirements without directly examining the data…