Related papers: A Framework for Private Matrix Analysis
We study the space complexity of the two related fields of differential privacy and adaptive data analysis. Specifically, (1) Under standard cryptographic assumptions, we show that there exists a problem P that requires exponentially more…
Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…
We present a federated, asynchronous, and $(\varepsilon, \delta)$-differentially private algorithm for PCA in the memory-limited setting. Our algorithm incrementally computes local model updates using a streaming procedure and adaptively…
Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…
In this work, we propose a differentially private algorithm for publishing matrices aggregated from sparse vectors. These matrices include social network adjacency matrices, user-item interaction matrices in recommendation systems, and…
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…
Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with…
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…
Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…
We study efficient distributed algorithms for the fundamental problem of principal component analysis and leading eigenvector computation on the sphere, when the data are randomly distributed among a set of computational nodes. We propose a…
Black-box machine learning models are used in critical decision-making domains, giving rise to several calls for more algorithmic transparency. The drawback is that model explanations can leak information about the training data and the…
In this paper, we study what price one has to pay to release {\em differentially private low-rank factorization} of a matrix. We consider various settings that are close to the real world applications of low-rank factorization: (i) the…
Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…
Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…
Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense…
Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large…
The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem…
In statistical disclosure control, the goal of data analysis is twofold: The released information must provide accurate and useful statistics about the underlying population of interest, while minimizing the potential for an individual…
Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this…
To preserve data privacy, multi-party computation (MPC) enables executing Machine Learning (ML) algorithms on private data. However, MPC frameworks do not include optimized operations on sparse data. This absence makes them unsuitable for…