Related papers: A Framework for Private Matrix Analysis
Privacy-preserving machine learning is learning from sensitive datasets that are typically distributed across multiple data owners. Private machine learning is a remarkable challenge in a large number of realistic scenarios where no trusted…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
Differentially Private algorithms often need to select the best amongst many candidate options. Classical works on this selection problem require that the candidates' goodness, measured as a real-valued score function, does not change by…
We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose…
In this brief, we present an enhanced privacy-preserving distributed estimation algorithm, referred to as the ``Double-Private Algorithm," which combines the principles of both differential privacy (DP) and cryptography. The proposed…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
In recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from their sum, $\mathbf{M}:= \mathbf{L} + \mathbf{S}$ and a provably exact…
In this paper, we address strongly convex programming for princi- pal component pursuit with reduced linear measurements, which decomposes a superposition of a low-rank matrix and a sparse matrix from a small set of linear measurements. We…
We provide the first provably joint differentially private algorithm with formal utility guarantees for the problem of user-level privacy-preserving collaborative filtering. Our algorithm is based on the Frank-Wolfe method, and it…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
We study sparse principal component analysis for high dimensional vector autoregressive time series under a doubly asymptotic framework, which allows the dimension $d$ to scale with the series length $T$. We treat the transition matrix of…
This paper proposes a differentially private recursive least squares algorithm to estimate the parameter of autoregressive systems with exogenous inputs and multi-participants (MP-ARX systems) and protect each participant's sensitive…
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…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
We study spectral graph clustering under edge differential privacy. We propose a matrix shuffling mechanism that combines randomized edge flipping with a random permutation of the adjacency matrix. While edge flipping alone provides only a…
Sparse variable selection improves interpretability and generalization in high-dimensional learning by selecting a small subset of informative features. Recent advances in Mixed Integer Programming (MIP) have enabled solving large-scale…
In this paper we propose a computationally efficient algorithm for on-line variable selection in multivariate regression problems involving high dimensional data streams. The algorithm recursively extracts all the latent factors of a…
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 differentially private (DP) estimation of a rank-$r$ matrix $M \in \mathbb{R}^{d_1\times d_2}$ under the trace regression model with Gaussian measurement matrices. Theoretically, the sensitivity of non-private spectral…
We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…