Related papers: Entropy Adjusted Graphical Lasso for Sparse Precis…

An algorithmic limit of compressed sensing or related variable-selection problems is analytically evaluated when a design matrix is given by an overcomplete random matrix. The replica method from statistical mechanics is employed to derive…

We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is…

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…

We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides…

We consider sparsity-based techniques for the approximation of high-dimensional functions from random pointwise evaluations. To date, almost all the works published in this field contain some a priori assumptions about the error corrupting…

The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…

The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $s\leq s^*\gamma$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $\gamma\geq 1$ is an…

Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…

Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…

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 many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching…

In exact sparse optimization problems on Rd (also known as sparsity constrained problems), one looks for solution that have few nonzero components. In this paper, we consider problems where sparsity is exactly measured either by the…

High-dimensional data sets are often analyzed and explored via the construction of a latent low-dimensional space which enables convenient visualization and efficient predictive modeling or clustering. For complex data structures, linear…

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of the central subspace. The new estimators use the Cholesky…

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…

Sparse estimation for Gaussian graphical models is a crucial technique for making the relationships among numerous observed variables more interpretable and quantifiable. Various methods have been proposed, including graphical lasso, which…

The sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse…

In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate…

We propose a new and computationally efficient algorithm for maximizing the observed log-likelihood for a multivariate normal data matrix with missing values. We show that our procedure based on iteratively regressing the missing on the…