Related papers: On the Sample Complexity of Privately Learning Unb…
The Gaussian mechanism is an essential building block used in multitude of differentially private data analysis algorithms. In this paper we revisit the Gaussian mechanism and show that the original analysis has several important…
This paper presents tight upper and lower bounds for minimum number of samples (copies of a quantum state) required to attain a prescribed accuracy (measured by error variance) for scalar parameters estimation using unbiased estimators…
We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper…
We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex…
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…
The complexity of learning a concept class under Gaussian marginals in the difficult agnostic model is closely related to its $L_1$-approximability by low-degree polynomials. For any concept class with Gaussian surface area at most…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
Learning the parameters of Gaussian mixture models is a fundamental and widely studied problem with numerous applications. In this work, we give new algorithms for learning the parameters of a high-dimensional, well separated, Gaussian…
We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…
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 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…
The Gaussian mechanism is one differential privacy mechanism commonly used to protect numerical data. However, it may be ill-suited to some applications because it has unbounded support and thus can produce invalid numerical answers to…
We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We study the problem of agnostic learning under the Gaussian distribution. We develop a method for finding hard families of examples for a wide class of problems by using LP duality. For Boolean-valued concept classes, we show that the…
We prove new upper and lower bounds on the sample complexity of $(\epsilon, \delta)$ differentially private algorithms for releasing approximate answers to threshold functions. A threshold function $c_x$ over a totally ordered domain $X$…
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 study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
We provide improved differentially private algorithms for identity testing of high-dimensional distributions. Specifically, for $d$-dimensional Gaussian distributions with known covariance $\Sigma$, we can test whether the distribution…
Understanding the relationship between generalization and privacy remains a central challenge in modern machine learning theory, particularly for deep networks trained by variants of differentially private stochastic gradient descent…