Related papers: On the Sample Complexity of Privately Learning Unb…
As increasing amounts of sensitive personal information is aggregated into data repositories, it has become important to develop mechanisms for processing the data without revealing information about individual data instances. The…
We study three problems that involve identifying homogeneous halfspaces under Gaussian distributions: agnostic learning, one-sided reliable learning, and fairness auditing. In each of these problems, we are given labeled examples…
We study statistical estimation under local differential privacy (LDP) when users may hold heterogeneous privacy levels and accuracy must be guaranteed with high probability. Departing from the common in-expectation analyses, and for…
We study the problem of learning nonparametric distributions in a finite mixture, and establish tight bounds on the sample complexity for learning the component distributions in such models. Namely, we are given i.i.d. samples from a pdf…
We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$. Under mild assumptions on the non-linearity, we obtain…
We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are "sub-Gaussian"~even when the randomness of the…
We give an example of a class of distributions that is learnable up to constant error in total variation distance with a finite number of samples, but not learnable under $(\varepsilon, \delta)$-differential privacy with the same target…
In this paper, we establish sample complexity bounds for learning high-dimensional simplices in $\mathbb{R}^K$ from noisy data. Specifically, we consider $n$ i.i.d. samples uniformly drawn from an unknown simplex in $\mathbb{R}^K$, each…
Learning high-dimensional distributions is a significant challenge in machine learning and statistics. Classical research has mostly concentrated on asymptotic analysis of such data under suitable assumptions. While existing works…
We give new characterizations of the sample complexity of answering linear queries (statistical queries) in the local and central models of differential privacy: *In the non-interactive local model, we give the first approximate…
In this work we analyze the sample complexity of classification by differentially private algorithms. Differential privacy is a strong and well-studied notion of privacy introduced by Dwork et al. (2006) that ensures that the output of an…
We investigate unbiased high-dimensional mean estimators in differential privacy. We consider differentially private mechanisms whose expected output equals the mean of the input dataset, for every dataset drawn from a fixed bounded…
Gaussian copulas are widely used to estimate multivariate distributions and relationships. We present algorithms for estimating Gaussian copula correlations that ensure differential privacy. We first convert data values into sets of two-way…
We construct a universally Bayes consistent learning rule that satisfies differential privacy (DP). We first handle the setting of binary classification and then extend our rule to the more general setting of density estimation (with…
We study the complexity of smoothed agnostic learning of halfspaces on $\{\pm 1\}^n$ under uniform marginals in the model of~\cite{KM25}, where each input coordinate is independently flipped with probability $\sigma \in (0, {1}/{2})$. We…
We study private prediction where differential privacy is achieved by adding noise to the outputs of a non-private model. Existing methods rely on noise proportional to the global sensitivity of the model, often resulting in sub-optimal…
We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…
We study the problem of estimating multivariate log-concave probability density functions. We prove the first sample complexity upper bound for learning log-concave densities on $\mathbb{R}^d$, for all $d \geq 1$. Prior to our work, no…
Differential Privacy (DP) provides tight upper bounds on the capabilities of optimal adversaries, but such adversaries are rarely encountered in practice. Under the hypothesis testing/membership inference interpretation of DP, we examine…
We introduce a simple framework for designing private boosting algorithms. We give natural conditions under which these algorithms are differentially private, efficient, and noise-tolerant PAC learners. To demonstrate our framework, we use…