Related papers: On Low-Space Differentially Private Low-rank Facto…

The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

This paper proposes a differentially private gradient-tracking-based distributed stochastic optimization algorithm over directed graphs. In particular, privacy noises are incorporated into each agent's state and tracking variable to…

Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank…

Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong…

A major challenge in applying differential privacy to training deep neural network models is scalability.The widely-used training algorithm, differentially private stochastic gradient descent (DP-SGD), struggles with training…

Large language models (LLMs) typically require fine-tuning for domain-specific tasks, and LoRA offers a computationally efficient approach by training low-rank adapters. LoRA is also communication-efficient for federated LLMs when multiple…

Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…

Regularized nonnegative low-rank approximations, such as sparse Nonnegative Matrix Factorization or sparse Nonnegative Tucker Decomposition, form an important branch of dimensionality reduction models known for their enhanced…

In this paper, we study the problem of estimating the covariance matrix under differential privacy, where the underlying covariance matrix is assumed to be sparse and of high dimensions. We propose a new method, called DP-Thresholding, to…

This paper presents a two-stage online algorithm for recovery of low-rank parameter matrix in non-stationary stochastic systems. The first stage applies the recursive least squares (RLS) estimator combined with its singular value…

Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…

Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…

Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…

The turnstile continual release model of differential privacy captures scenarios where a privacy-preserving real-time analysis is sought for a dataset evolving through additions and deletions. In typical applications of real-time data…

Kernel methods represent some of the most popular machine learning tools for data analysis. Since exact kernel methods can be prohibitively expensive for large problems, reliable low-rank matrix approximations and high-performance…

Recently differential privacy has been used for a number of streaming, data structure, and dynamic graph problems as a means of hiding the internal randomness of the data structure, so that multiple possibly adaptive queries can be made…

Low-rank matrix regression refers to the instances of recovering a low-rank matrix based on specially designed measurements and the corresponding noisy outcomes. In the last decade, numerous statistical methodologies have been developed for…

Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…

Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…