Related papers: SLS (Single $\ell_1$ Selection): a new greedy algo…
Recently, greedy algorithm has received much attention as a cost-effective means to reconstruct the sparse signals from compressed measurements. Much of previous work has focused on the investigation of a single candidate to identify the…
We focus on solving the clustered lasso problem, which is a least squares problem with the $\ell_1$-type penalties imposed on both the coefficients and their pairwise differences to learn the group structure of the regression parameters.…
Imposition of a lasso penalty shrinks parameter estimates toward zero and performs continuous model selection. Lasso penalized regression is capable of handling linear regression problems where the number of predictors far exceeds the…
Deepening and widening convolutional neural networks (CNNs) significantly increases the number of trainable weight parameters by adding more convolutional layers and feature maps per layer, respectively. By imposing inter- and intra-group…
In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study,…
Broadband wireless channels usually have the sparse nature. Based on the assumption of Gaussian noise model, adaptive filtering algorithms for reconstruction sparse channels were proposed to take advantage of channel sparsity. However,…
The proportionate normalized least mean square (PNLMS) algorithm and its variants are by far the most popular adaptive filters that are used to identify sparse systems. The convergence speed of the PNLMS algorithm, though very high…
Various $\ell_1$-penalised estimation methods such as graphical lasso and CLIME are widely used for sparse precision matrix estimation. Many of these methods have been shown to be consistent under various quantitative assumptions about the…
The Column Subset Selection Problem provides a natural framework for unsupervised feature selection. Despite being a hard combinatorial optimization problem, there exist efficient algorithms that provide good approximations. The drawback of…
Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=X\theta^*+w$ for a $k$-sparse vector $\theta^*$ (that is, $\|\theta^*\|_0\leq…
We consider solving the $\ell_1$-regularized least-squares ($\ell_1$-LS) problem in the context of sparse recovery, for applications such as compressed sensing. The standard proximal gradient method, also known as iterative…
A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modeling method while it has been known to yield unexpected large bias especially at a sparse…
In this paper, we propose a novel sparse learning based feature selection method that directly optimizes a large margin linear classification model sparsity with l_(2,p)-norm (0 < p < 1)subject to data-fitting constraints, rather than using…
We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the…
The most widely used form of convolutional sparse coding uses an $\ell_1$ regularization term. While this approach has been successful in a variety of applications, a limitation of the $\ell_1$ penalty is that it is homogeneous across the…
We study the problem of estimating a random process from the observations collected by a network of sensors that operate under resource constraints. When the dynamics of the process and sensor observations are described by a state-space…
We propose a new random pruning method (called "submodular sparsification (SS)") to reduce the cost of submodular maximization. The pruning is applied via a "submodularity graph" over the $n$ ground elements, where each directed edge is…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…
The subspace selection problem seeks a subspace that maximizes an objective function under some constraint. This problem includes several important machine learning problems such as the principal component analysis and sparse dictionary…
The uncertainty quantification and error control of classifiers are crucial in many high-consequence decision-making scenarios. We propose a selective classification framework that provides an indecision option for any observations that…