相关论文: Randomness Efficient Fast-Johnson-Lindenstrauss Tr…

We give two different and simple constructions for dimensionality reduction in $\ell_2$ via linear mappings that are sparse: only an $O(\varepsilon)$-fraction of entries in each column of our embedding matrices are non-zero to achieve…

For a set $X$ of $N$ points in $\mathbb{R}^D$, the Johnson-Lindenstrauss lemma provides random linear maps that approximately preserve all pairwise distances in $X$ -- up to multiplicative error $(1\pm \epsilon)$ with high probability --…

Privacy concerns with sensitive data are receiving increasing attention. In this paper, we study local differential privacy (LDP) in interactive decentralized optimization. By constructing random local aggregators, we propose a framework to…

The Johnson-Lindenstrauss lemma is one of the corner stone results in dimensionality reduction. It says that given $N$, for any set of $N$ vectors $X \subset \mathbb{R}^n$, there exists a mapping $f : X \to \mathbb{R}^m$ such that $f(X)$…

Computing accurate low rank approximations of large matrices is a fundamental data mining task. In many applications however the matrix contains sensitive information about individuals. In such case we would like to release a low rank…

Recent work of [Dasgupta-Kumar-Sarlos, STOC 2010] gave a sparse Johnson-Lindenstrauss transform and left as a main open question whether their construction could be efficiently derandomized. We answer their question affirmatively by giving…

We investigate the local differential privacy (LDP) guarantees of a randomized privacy mechanism via its contraction properties. We first show that LDP constraints can be equivalently cast in terms of the contraction coefficient of the…

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…

Differential privacy (DP) has emerged as a de facto standard privacy notion for a wide range of applications. Since the meaning of data utility in different applications may vastly differ, a key challenge is to find the optimal…

We prove the Johnson-Lindenstrauss property for matrices $\Phi D_\xi$ where $\Phi$ has the restricted isometry property and $D_\xi$ is a diagonal matrix containing the entries of a Kronecker product $\xi = \xi^{(1)} \otimes \dots \otimes…

We study the problem of differentially private second moment estimation and present a new algorithm that achieve strong privacy-utility trade-offs even for worst-case inputs under subsamplability assumptions on the data. We call an input…

Motivated by the problem of compressing point sets into as few bits as possible while maintaining information about approximate distances between points, we construct random nonlinear maps $\varphi_\ell$ that compress point sets in the…

Allen-Zhu, Gelashvili, Micali, and Shavit construct a sparse, sign-consistent Johnson-Lindenstrauss distribution, and prove that this distribution yields an essentially optimal dimension for the correct choice of sparsity. However, their…

We establish a simple connection between robust and differentially-private algorithms: private mechanisms which perform well with very high probability are automatically robust in the sense that they retain accuracy even if a constant…

We study the problem of differentially private (DP) matrix completion under user-level privacy. We design a joint differentially private variant of the popular Alternating-Least-Squares (ALS) method that achieves: i) (nearly) optimal sample…

We investigate the problems of identity and closeness testing over a discrete population from random samples. Our goal is to develop efficient testers while guaranteeing Differential Privacy to the individuals of the population. We describe…

Patterned random matrices such as the reverse circulant, the symmetric circulant, the Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD), have attracted much attention. Under the assumption that the…

The Johnson-Lindenstrauss transform allows one to embed a dataset of $n$ points in $\mathbb{R}^d$ into $\mathbb{R}^m,$ while preserving the pairwise distance between any pair of points up to a factor $(1 \pm \varepsilon)$, provided that $m…

We introduce three differentially-private algorithms that approximates the 2nd-moment matrix of the data. These algorithm, which in contrast to existing algorithms output positive-definite matrices, correspond to existing techniques in…

The ubiquity of distributed machine learning (ML) in sensitive public domain applications calls for algorithms that protect data privacy, while being robust to faults and adversarial behaviors. Although privacy and robustness have been…