Related papers: Randomly sparsified Richardson iteration: A dimens…
This paper proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalised diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the…
We describe a new library named picasso, which implements a unified framework of pathwise coordinate optimization for a variety of sparse learning problems (e.g., sparse linear regression, sparse logistic regression, sparse Poisson…
We introduce a generic framework for solving linear programs (LPs) with many constraints $(n \gg d)$ via adaptive sparsification. Our approach provides a principled generalization of the techniques of [Assadi '23] from matching problems to…
The Kaczmarz algorithm is a popular solver for overdetermined linear systems due to its simplicity and speed. In this paper, we propose a modification that speeds up the convergence of the randomized Kaczmarz algorithm for systems of linear…
Random projection is often used to project higher-dimensional vectors onto a lower-dimensional space, while approximately preserving their pairwise distances. It has emerged as a powerful tool in various data processing tasks and has…
We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally - that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in…
Regularized methods have been widely applied to system identification problems without known model structures. This paper proposes an infinite-dimensional sparse learning algorithm based on atomic norm regularization. Atomic norm…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression…
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse…
Recently there has been much interest in "sparsifying" sums of rank one matrices: modifying the coefficients such that only a few are nonzero, while approximately preserving the matrix that results from the sum. Results of this sort have…
We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker,…
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the…
We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…
In many statistical modeling problems, such as classification and regression, it is common to encounter sparse and blocky coefficients. Sparse fused Lasso is specifically designed to recover these sparse and blocky structured features,…
In this paper, we consider a recursive estimation problem for linear regression where the signal to be estimated admits a sparse representation and measurement samples are only sequentially available. We propose a convergent parallel…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…