Related papers: Efficient approximation of sparse Jacobians for ti…
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
In this paper, we adapt the geodesic distance-based recursive filter to the sparse data interpolation problem. The proposed technique is general and can be easily applied to any kind of sparse data. We demonstrate the superiority over other…
We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal…
We study polynomial-time approximation algorithms for (edge/vertex) Sparsest Cut and Small Set Expansion in terms of $k$, the number of edges or vertices cut in the optimal solution. Our main results are $\mathcal{O}(\text{polylog}\,…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems…
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…
This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…
Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e. for computing a few of largest singular values and the corresponding singular vectors), a dynamically shifted power…
Accurate, high-resolution, and real-time DOA estimation is a cornerstone of environmental perception in automotive radar systems. While sparse signal recovery techniques offer super-resolution and high-precision estimation, their…
Engineering simulations are usually based on complex, grid-based, or mesh-free methods for solving partial differential equations. The results of these methods cover large fields of physical quantities at very many discrete spatial…
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…
We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…
Sparse arrays have been widely exploited in radar systems because of their advantages in achieving large array aperture at low hardware cost, while significantly reducing mutual coupling. However, sparse arrays suffer from high sidelobes…
In this pedagogical article, we present a simple direct matrix method for analytically computing the Jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integro-differential equations. The method is…
In applied Bayesian inference scenarios, users may have access to a large number of pre-existing model evaluations, for example from maximum-a-posteriori (MAP) optimization runs. However, traditional approximate inference techniques make…
Compression is a crucial solution for data reduction in modern scientific applications due to the exponential growth of data from simulations, experiments, and observations. Compression with progressive retrieval capability allows users to…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
Recently several methods were proposed for sparse optimization which make careful use of second-order information [10, 28, 16, 3] to improve local convergence rates. These methods construct a composite quadratic approximation using Hessian…