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We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…

Machine Learning · Statistics 2012-06-08 Ali Jalali , Sujay Sanghavi

Recent studies have demonstrated improved skill in numerical weather prediction via the use of spatially correlated observation error covariance information in data assimilation systems. In this case, the observation weighting matrices…

Numerical Analysis · Mathematics 2022-01-05 Guannan Hu , Sarah L. Dance

We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…

Machine Learning · Computer Science 2012-07-03 Haim Avron , Satyen Kale , Shiva Kasiviswanathan , Vikas Sindhwani

The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…

Information Theory · Computer Science 2018-10-23 Ali Çivril

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…

Machine Learning · Computer Science 2016-03-30 Luc Le Magoarou , Rémi Gribonval

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…

Machine Learning · Statistics 2021-06-08 Antoine Dedieu , Hussein Hazimeh , Rahul Mazumder

In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…

Numerical Analysis · Mathematics 2016-02-11 Yariv Aizenbud , Amir Averbuch

The modified Cholesky decomposition is commonly used for precision matrix estimation given a specified order of random variables. However, the order of variables is often not available or cannot be pre-determined. In this work, we propose…

Machine Learning · Statistics 2021-11-23 Xiaoning Kang , Xinwei Deng

Sparsity regularization has garnered significant interest across multiple disciplines, including statistics, imaging, and signal processing. Standard techniques for addressing sparsity regularization include iterative soft thresholding…

Optimization and Control · Mathematics 2025-06-16 Long Li , Liang Ding

In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that near-optimal approximation error can nevertheless be…

Numerical Analysis · Mathematics 2024-02-14 Abdellah Chkifa , Matthieu Dolbeault

Constructing a propagation map from a set of scattered measurements finds important applications in many areas, such as localization, spectrum monitoring and management. Classical interpolation-type methods have poor performance in regions…

Signal Processing · Electrical Eng. & Systems 2023-01-25 Hao Sun , Junting Chen

Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsity generalization of the dense tensor BR1Approx, and is a higher-order extension of the sparse matrix BR1Approx, is one of the most important problems in sparse tensor…

Numerical Analysis · Mathematics 2022-07-15 Xianpeng Mao , Yuning Yang

Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…

Numerical Analysis · Mathematics 2020-12-14 Alec Michael Dunton , Alyson Fox

Generally, discretization of partial differential equations (PDEs) creates a sequence of linear systems $A_k x_k = b_k, k = 0, 1, 2, ..., N$ with well-known and structured sparsity patterns. Preconditioners are often necessary to achieve…

Numerical Analysis · Mathematics 2024-06-26 Rishad Islam , Arielle Carr , Colin Jacobs

In this paper, we show a way to exploit sparsity in the problem data in a primal-dual potential reduction method for solving a class of semidefinite programs. When the problem data is sparse, the dual variable is also sparse, but the primal…

Numerical Analysis · Mathematics 2025-10-20 Gun Srijuntongsiri , Stephen A. Vavasis

In post--layout circuit simulation, efficient model order reduction (MOR) for many--port resistor--capacitor (RC) circuits remains a crucial issue. The current mainstream MOR methods for such circuits include high--order moment matching…

Systems and Control · Electrical Eng. & Systems 2025-10-21 Siyuan Yin , Yuncheng Xu , Lin Liu , Fan Yang , Xuan Zeng , Chengtao An , Yangfeng Su

The SPAI algorithm, a sparse approximate inverse preconditioning technique for large sparse linear systems, proposed by Grote and Huckle [SIAM J. Sci. Comput., 18 (1997), pp.~838--853.], is based on the F-norm minimization and computes a…

Numerical Analysis · Mathematics 2018-08-29 Zhongxiao Jia , Wenjie Kang

We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with…

Numerical Analysis · Computer Science 2012-09-05 Nicolas Bock , Matt Challacombe

We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding…

Methodology · Statistics 2026-02-06 Mitra Kharabati , Morteza Amini , Mohammad Arashi