Related papers: Wishart Mechanism for Differentially Private Princ…
We introduce the (Wishart) projection mechanism, a randomized map of the form $S \mapsto M f(S)$ with $M \sim W_d(1/r I_d, r)$ and study its differential privacy properties. For vector-valued queries $f$, we prove non-asymptotic DP…
This paper presents a new discretization error quantification method for the numerical integration of ordinary differential equations. The error is modelled by using the Wishart distribution, which enables us to capture the correlation…
Currently known methods for this task either employ the computationally intensive \emph{exponential mechanism} or require an access to the covariance matrix, and therefore fail to utilize potential sparsity of the data. The problem of…
In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations…
Traditionally, differential privacy mechanism design has been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding…
Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding…
In an MPC-protected distributed computation, although the use of MPC assures data privacy during computation, sensitive information may still be inferred by curious MPC participants from the computation output. This can be observed, for…
Principal Component Analysis (PCA) is a pivotal technique widely utilized in the realms of machine learning and data analysis. It aims to reduce the dimensionality of a dataset while minimizing the loss of information. In recent years,…
In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the…
In this paper, we focus on developing a novel mechanism to preserve differential privacy in deep neural networks, such that: (1) The privacy budget consumption is totally independent of the number of training steps; (2) It has the ability…
There is an increasing demand to make data "open" to third parties, as data sharing has great benefits in data-driven decision making. However, with a wide variety of sensitive data collected, protecting privacy of individuals, communities…
We revisit the input perturbations framework for differential privacy where noise is added to the input $A\in \mathcal{S}$ and the result is then projected back to the space of admissible datasets $\mathcal{S}$. Through this framework, we…
We adapt the canonical Laplace mechanism, widely used in differentially private data analysis, to achieve near instance optimality with respect to the hardness of the underlying dataset. In particular, we construct a piecewise Laplace…
Principal component analysis (PCA) is a well-known tool in multivariate statistics. One significant challenge in using PCA is the choice of the number of components. In order to address this challenge, we propose an exact distribution-based…
Based on a student research project this article gives a short review on Wishart processes. A Wishart procces is a matrix valued continuous time stochastic process with a marginal Wishart distribution. The Wishart distribution is a matrix…
We revisit the task of computing the span of the top $r$ singular vectors $u_1, \ldots, u_r$ of a matrix under differential privacy. We show that a simple and efficient algorithm -- based on singular value decomposition and standard…
The framework of differential privacy protects an individual's privacy while publishing query responses on congregated data. In this work, a new noise addition mechanism for differential privacy is introduced where the noise added is…
We study private matrix analysis in the sliding window model where only the last $W$ updates to matrices are considered useful for analysis. We give first efficient $o(W)$ space differentially private algorithms for spectral approximation,…
Performing low-rank matrix completion with sensitive user data calls for privacy-preserving approaches. In this work, we propose a novel noise addition mechanism for preserving differential privacy where the noise distribution is inspired…
Differential privacy mechanisms such as the Gaussian or Laplace mechanism have been widely used in data analytics for preserving individual privacy. However, they are mostly designed for continuous outputs and are unsuitable for scenarios…