Related papers: Localized spectrum slicing

A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…

Boosting as gradient descent algorithms is one popular method in machine learning. In this paper a novel Boosting-type algorithm is proposed based on restricted gradient descent with structural sparsity control whose underlying dynamics are…

We present a local Fourier slice equation that enables local and sparse projection of a signal. Our result exploits that a slice in frequency space is an iso-parameter set in spherical coordinates. Therefore, the projection of suitable…

We consider the uniform approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix by that of a smaller counterpart obtained through projections. The projection subspaces are constructed iteratively by means of…

Self-supervised learning (SSL) has emerged as a powerful strategy for representation learning under limited annotation regimes, yet its effectiveness remains highly sensitive to many factors, especially the nature of the target task. In…

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…

This paper introduces the localized sparsifying preconditioner for the pseudospectral approximations of indefinite systems on periodic structures. The work is built on top of the recently proposed sparsifying preconditioner with two major…

Sparse decomposition has been widely used for different applications, such as source separation, image classification and image denoising. This paper presents a new algorithm for segmentation of an image into background and foreground text…

We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the…

We propose a localized divide and conquer algorithm for inverse factorization $S^{-1} = ZZ^*$ of Hermitian positive definite matrices $S$ with localized structure, e.g. exponential decay with respect to some given distance function on the…

High-dimensional sparse data present computational and statistical challenges for supervised learning. We propose compact linear sketches for reducing the dimensionality of the input, followed by a single layer neural network. We show that…

In this paper we use some basic facts from the theory of (matrix) Lie groups and algebras to show that many of the classical matrix splittings used to construct stationary iterative methods and preconditioniers for Krylov subspace methods…

In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…

There are a large number of methods for solving under-determined linear inverse problem. Many of them have very high time complexity for large datasets. We propose a new method called Two-Stage Sparse Representation (TSSR) to tackle this…

The debiased estimator is a crucial tool in statistical inference for high-dimensional model parameters. However, constructing such an estimator involves estimating the high-dimensional inverse Hessian matrix, incurring significant…

We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…

In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed…

This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and…

We provide a systematic deterministic numerical scheme to approximate the volume (i.e. the Lebesgue measure) of a basic semi-algebraic set whose description follows a sparsity pattern. As in previous works (without sparsity), the underlying…

This paper studies the subspace segmentation problem. Given a set of data points drawn from a union of subspaces, the goal is to partition them into their underlying subspaces they were drawn from. The spectral clustering method is used as…