Related papers: Fast L1-Minimization Algorithm for Sparse Approxim…

This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local…

In sparse information recovery, the core problem is to solve the $l_0$-minimization which is NP-hard. On one hand, in order to recover the original sparse solution, there are a lot of papers designing alternative model for…

When applying principal component analysis (PCA) for dimension reduction, the most varying projections are usually used in order to retain most of the information. For the purpose of anomaly and change detection, however, the least varying…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

Recurrent Neural Networks and in particular Long Short-Term Memory (LSTM) networks have demonstrated state-of-the-art accuracy in several emerging Artificial Intelligence tasks. However, the models are becoming increasingly demanding in…

Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…

We introduce an extension to the CLRS algorithmic learning benchmark, prioritizing scalability and the utilization of sparse representations. Many algorithms in CLRS require global memory or information exchange, mirrored in its execution…

The $L_1$-regularized models are widely used for sparse regression or classification tasks. In this paper, we propose the orthant-wise passive descent algorithm (OPDA) for optimizing $L_1$-regularized models, as an improved substitute of…

We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…

We consider sparse matrix estimation where the goal is to estimate an $n\times n$ matrix from noisy observations of a small subset of its entries. We analyze the estimation error of the popularly utilized collaborative filtering algorithm…

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…

Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…

We study the properties of sparse reconstruction of transformed $\ell_1$ (TL1) minimization and present improved theoretical results about the recoverability and the accuracy of this reconstruction from undersampled measurements. We then…

Fan and Li propose a family of variable selection methods via penalized likelihood using concave penalty functions. The nonconcave penalized likelihood estimators enjoy the oracle properties, but maximizing the penalized likelihood function…

Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…

We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l1-norm penalty function on the filter…

In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…