Related papers: Private Distribution Learning with Public Data: Th…
We study the problem of estimating mixtures of Gaussians under the constraint of differential privacy (DP). Our main result is that $\text{poly}(k,d,1/\alpha,1/\varepsilon,\log(1/\delta))$ samples are sufficient to estimate a mixture of $k$…
Given a dataset of $n$ i.i.d. samples from an unknown distribution $P$, we consider the problem of generating a sample from a distribution that is close to $P$ in total variation distance, under the constraint of differential privacy (DP).…
We initiate the study of a new model of supervised learning under privacy constraints. Imagine a medical study where a dataset is sampled from a population of both healthy and unhealthy individuals. Suppose healthy individuals have no…
We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…
The most effective differentially private machine learning algorithms in practice rely on an additional source of purportedly public data. This paradigm is most interesting when the two sources combine to be more than the sum of their…
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 initiate an investigation of private sampling from distributions. Given a dataset with $n$ independent observations from an unknown distribution $P$, a sampling algorithm must output a single observation from a distribution that is close…
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…
We consider the problem of learning mixtures of Gaussians under the constraint of approximate differential privacy. We prove that $\widetilde{O}(k^2 d \log^{3/2}(1/\delta) / \alpha^2 \varepsilon)$ samples are sufficient to learn a mixture…
We study a basic private estimation problem: each of $n$ users draws a single i.i.d. sample from an unknown Gaussian distribution, and the goal is to estimate the mean of this Gaussian distribution while satisfying local differential…
We present novel, computationally efficient, and differentially private algorithms for two fundamental high-dimensional learning problems: learning a multivariate Gaussian and learning a product distribution over the Boolean hypercube in…
We consider learning problems where the training set consists of two types of examples: private and public. The goal is to design a learning algorithm that satisfies differential privacy only with respect to the private examples. This…
This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…
A private learner is an algorithm that given a sample of labeled individual examples outputs a generalizing hypothesis while preserving the privacy of each individual. In 2008, Kasiviswanathan et al. (FOCS 2008) gave a generic construction…
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…
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…
In 2008, Kasiviswanathan et al. defined private learning as a combination of PAC learning and differential privacy. Informally, a private learner is applied to a collection of labeled individual information and outputs a hypothesis while…
We study a class of private learning problems in which the data is a join of private and public features. This is often the case in private personalization tasks such as recommendation or ad prediction, in which features related to…
In Semi-Supervised Semi-Private (SP) learning, the learner has access to both public unlabelled and private labelled data. We propose a computationally efficient algorithm that, under mild assumptions on the data, provably achieves…
Learning problems form an important category of computational tasks that generalizes many of the computations researchers apply to large real-life data sets. We ask: what concept classes can be learned privately, namely, by an algorithm…