Related papers: On Differentially Private Subspace Estimation in a…
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 study the space complexity of the two related fields of differential privacy and adaptive data analysis. Specifically, (1) Under standard cryptographic assumptions, we show that there exists a problem P that requires exponentially more…
We initiate the study of differentially private (DP) estimation with access to a small amount of public data. For private estimation of d-dimensional Gaussians, we assume that the public data comes from a Gaussian that may have vanishing…
It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…
In this work, we study high-dimensional mean estimation under user-level differential privacy, and design an $(\varepsilon,\delta)$-differentially private mechanism using as few users as possible. In particular, we provide a nearly optimal…
Constructing a differentially private (DP) estimator requires deriving the maximum influence of an observation, which can be difficult in the absence of exogenous bounds on the input data or the estimator, especially in high dimensional…
Real-world datasets are often of high dimension and effected by the curse of dimensionality. This hinders their comprehensibility and interpretability. To reduce the complexity feature selection aims to identify features that are crucial to…
Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental…
We study the sample complexity of learning threshold functions under the constraint of differential privacy. It is assumed that each labeled example in the training data is the information of one individual and we would like to come up with…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
In modern settings of data analysis, we may be running our algorithms on datasets that are sensitive in nature. However, classical machine learning and statistical algorithms were not designed with these risks in mind, and it has been…
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…
The last few years have seen a surge of work on high dimensional statistics under privacy constraints, mostly following two main lines of work: the ``worst case'' line, which does not make any distributional assumptions on the input data;…
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
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…
We study differentially private mean estimation in a high-dimensional setting. Existing differential privacy techniques applied to large dimensions lead to computationally intractable problems or estimators with excessive privacy loss.…
The curse of dimensionality has remained a challenge for a wide variety of algorithms in data mining, clustering, classification and privacy. Recently, it was shown that an increasing dimensionality makes the data resistant to effective…
Differentially private stochastic gradient descent privatizes model training by injecting noise into each iteration, where the noise magnitude increases with the number of model parameters. Recent works suggest that we can reduce the noise…
Differentially private federated learning is crucial for maintaining privacy in distributed environments. This paper investigates the challenges of high-dimensional estimation and inference under the constraints of differential privacy.…
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…