Related papers: An Iterative Algorithm for Differentially Private …
This paper proposes new methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We first introduce a DP Bayesian Information Criterion (DP-BIC) for selecting the…
Posterior sampling, i.e., exponential mechanism to sample from the posterior distribution, provides $\varepsilon$-pure differential privacy (DP) guarantees and does not suffer from potentially unbounded privacy breach introduced by…
Differentially Private Stochastic Gradient Descent (DP-SGD) is the dominant paradigm for private training, but its fundamental limitations under worst-case adversarial privacy definitions remain poorly understood. We analyze DP-SGD in the…
In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue…
We design a new algorithm for the Euclidean $k$-means problem that operates in the local model of differential privacy. Unlike in the non-private literature, differentially private algorithms for the $k$-means objective incur both additive…
We consider differentially private approximate singular vector computation. Known worst-case lower bounds show that the error of any differentially private algorithm must scale polynomially with the dimension of the singular vector. We are…
In this paper we tackle the challenge of making the stochastic coordinate descent algorithm differentially private. Compared to the classical gradient descent algorithm where updates operate on a single model vector and controlled noise…
We present two sample-efficient differentially private mean estimators for $d$-dimensional (sub)Gaussian distributions with unknown covariance. Informally, given $n \gtrsim d/\alpha^2$ samples from such a distribution with mean $\mu$ and…
Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…
Personalized privacy becomes critical in deep learning for Trustworthy AI. While Differentially Private Stochastic Gradient Descent (DP-SGD) is widely used in deep learning methods supporting privacy, it provides the same level of privacy…
This paper develops a framework for differentially private $e$-values under Gaussian differential privacy ($\mu$-GDP). We characterize the canonical noise mechanism, establishing that optimal multiplicative perturbation follows a Gaussian…
We consider a platform's problem of collecting data from privacy sensitive users to estimate an underlying parameter of interest. We formulate this question as a Bayesian-optimal mechanism design problem, in which an individual can share…
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,…
Sparse Principal Component Analysis (SPCA) is a fundamental technique for dimensionality reduction, and is NP-hard. In this paper, we introduce a randomized approximation algorithm for SPCA, which is based on the basic SDP relaxation. Our…
The Alternating Direction Method of Multipliers (ADMM) and its distributed version have been widely used in machine learning. In the iterations of ADMM, model updates using local private data and model exchanges among agents impose critical…
Given an integer $k\geq1$ and a set $P$ of $n$ points in $\REAL^d$, the classic $k$-PCA (Principle Component Analysis) approximates the affine \emph{$k$-subspace mean} of $P$, which is the $k$-dimensional affine linear subspace that…
Training machine learning models with differential privacy (DP) has received increasing interest in recent years. One of the most popular algorithms for training differentially private models is differentially private stochastic gradient…
In this paper, we investigate the problem of differentially private distributed optimization. Recognizing that lower sensitivity leads to higher accuracy, we analyze the key factors influencing the sensitivity of differentially private…