Related papers: Differentially Private Low-dimensional Synthetic D…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…
Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…
Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
In this paper, we study differentially private (DP) algorithms for computing the geometric median (GM) of a dataset: Given $n$ points, $x_1,\dots,x_n$ in $\mathbb{R}^d$, the goal is to find a point $\theta$ that minimizes the sum of the…
A basic problem in the design of privacy-preserving algorithms is the private maximization problem: the goal is to pick an item from a universe that (approximately) maximizes a data-dependent function, all under the constraint of…
A representative model in integrative analysis of two high-dimensional correlated datasets is to decompose each data matrix into a low-rank common matrix generated by latent factors shared across datasets, a low-rank distinctive matrix…
Private data analysis faces a significant challenge known as the curse of dimensionality, leading to increased costs. However, many datasets possess an inherent low-dimensional structure. For instance, during optimization via gradient…
We introduce an $(\epsilon, \delta)$-jointly differentially private algorithm for packing problems. Our algorithm not only achieves the optimal trade-off between the privacy parameter $\epsilon$ and the minimum supply requirement (up to…
We study the problem of differentially private optimization with linear constraints when the right-hand-side of the constraints depends on private data. This type of problem appears in many applications, especially resource allocation.…
The purpose of this paper is to develop a mathematical analysis theory to solve differential privacy problems. The heart of our approaches is to use analytic tools to characterize the correlations among the outputs of different datasets,…
Conformal prediction (CP) has attracted broad attention as a simple and flexible framework for uncertainty quantification through prediction sets. In this work, we study how to deploy CP under differential privacy (DP) in a statistically…
Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between…
Differentially private (DP) synthetic data generation is a practical method for improving access to data as a means to encourage productive partnerships. One issue inherent to DP is that the "privacy budget" is generally "spent" evenly…
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…
Substantial quantity and high quality are the golden rules of making a good training dataset with sample privacy protection equally important. Generating synthetic samples that resemble high-quality private data while ensuring Differential…
Many data producers seek to provide users access to confidential data without unduly compromising data subjects' privacy and confidentiality. One general strategy is to require users to do analyses without seeing the confidential data; for…
Differential privacy is a widely adopted framework designed to safeguard the sensitive information of data providers within a data set. It is based on the application of controlled noise at the interface between the server that stores and…
The availability of rich and vast data sources has greatly advanced machine learning applications in various domains. However, data with privacy concerns comes with stringent regulations that frequently prohibited data access and data…
Methods for analysis of principal components in discrete data have existed for some time under various names such as grade of membership modelling, probabilistic latent semantic analysis, and genotype inference with admixture. In this paper…