Related papers: Private High-Dimensional Hypothesis Testing
We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\tilde O(\sqrt{n}\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability…
A recent line of work initiated by Chiesa and Gur and further developed by Herman and Rothblum investigates the sample and communication complexity of verifying properties of distributions with the assistance of a powerful, knowledgeable,…
With changes in privacy laws, there is often a hard requirement for client data to remain on the device rather than being sent to the server. Therefore, most processing happens on the device, and only an altered element is sent to the…
We study the problem of estimating a set of $d$ linear queries with respect to some unknown distribution $\mathbf{p}$ over a domain $\mathcal{J}=[J]$ based on a sensitive data set of $n$ individuals under the constraint of local…
A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…
We find separation rates for testing multinomial or more general discrete distributions under the constraint of local differential privacy. We construct efficient randomized algorithms and test procedures, in both the case where only…
A new line of work, started with Dwork et al., studies the task of answering statistical queries using a sample and relates the problem to the concept of differential privacy. By the Hoeffding bound, a sample of size $O(\log k/\alpha^2)$…
The Gaussian distribution is widely used in mechanism design for differential privacy (DP). Thanks to its sub-Gaussian tail, it significantly reduces the chance of outliers when responding to queries. However, it can only provide…
We study hypothesis testing (aka state certification) in the non-identically distributed setting. A recent work (Garg et al. 2023) considered the classical case, in which one is given (independent) samples from $T$ unknown probability…
We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…
Distribution testing deals with what information can be deduced about an unknown distribution over $\{1,\ldots,n\}$, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In…
We study simple binary hypothesis testing under both local differential privacy (LDP) and communication constraints. We qualify our results as either minimax optimal or instance optimal: the former hold for the set of distribution pairs…
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…
We study the problem of learning mixtures of Gaussians with approximate differential privacy. We prove that roughly $kd^2 + k^{1.5} d^{1.75} + k^2 d$ samples suffice to learn a mixture of $k$ arbitrary $d$-dimensional Gaussians up to low…
We develop a near-optimal testing procedure under the framework of Gaussian differential privacy for simple as well as one- and two-sided tests under monotone likelihood ratio conditions. Our mechanism is based on a private mean estimator…
Hypothesis testing is a central problem in statistical analysis, and there is currently a lack of differentially private tests which are both statistically valid and powerful. In this paper, we develop several new differentially private…
In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
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…
Gaussian smoothed sliced Wasserstein distance has been recently introduced for comparing probability distributions, while preserving privacy on the data. It has been shown that it provides performances similar to its non-smoothed…