Related papers: Beyond Worst-Case Analysis in Private Singular Vec…
Fingerprinting arguments, first introduced by Bun, Ullman, and Vadhan (STOC 2014), are the most widely used method for establishing lower bounds on the sample complexity or error of approximately differentially private (DP) algorithms.…
We study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…
In the worst-case analysis of algorithms, the overall performance of an algorithm is summarized by its worst performance on any input. This approach has countless success stories, but there are also important computational problems --- like…
A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…
We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…
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 present a new locally differentially private algorithm for the heavy hitters problem which achieves optimal worst-case error as a function of all standardly considered parameters. Prior work obtained error rates which depend optimally on…
Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which…
Hierarchical Clustering is a popular unsupervised machine learning method with decades of history and numerous applications. We initiate the study of differentially private approximation algorithms for hierarchical clustering under the…
Developing a differentially private deep learning algorithm is challenging, due to the difficulty in analyzing the sensitivity of objective functions that are typically used to train deep neural networks. Many existing methods resort to the…
We study fine-grained error bounds for differentially private algorithms for counting under continual observation. Our main insight is that the matrix mechanism when using lower-triangular matrices can be used in the continual observation…
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 new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
Given a matrix $A$ and iteration step $k$, we study a best possible attainable upper bound on the GMRES residual norm that does not depend on the initial vector $b$. This quantity is called the worst-case GMRES approximation. We show that…
The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private…
Through the lens of information-theoretic reductions, we examine a reductions approach to fair optimization and learning where a black-box optimizer is used to learn a fair model for classification or regression. Quantifying the complexity,…
We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the…
We study the statistical complexity of private linear regression under an unknown, potentially ill-conditioned covariate distribution. Somewhat surprisingly, under privacy constraints the intrinsic complexity is \emph{not} captured by the…
A central challenge in machine learning is to understand how noise or measurement errors affect low-rank approximations, particularly in the spectral norm. This question is especially important in differentially private low-rank…
A common goal of privacy research is to release synthetic data that satisfies a formal privacy guarantee and can be used by an analyst in place of the original data. To achieve reasonable accuracy, a synthetic data set must be tuned to…