Related papers: A linear programming approach to sparse linear reg…

The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…

Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…

We proposed a new penalized method in this paper to solve sparse Poisson Regression problems. Being different from $\ell_1$ penalized log-likelihood estimation, our new method can be viewed as penalized weighted score function method. We…

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 high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…

We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the…

In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now those corresponding non-convex algorithms lack convergence guarantees from the initial…

This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…

Recently, classical kernel methods have been extended by the introduction of suitable tensor kernels so to promote sparsity in the solution of the underlying regression problem. Indeed, they solve an lp-norm regularization problem, with…

In this work, we propose an algorithm for solving exact sparse linear regression problems over a network in a distributed manner. Particularly, we consider the problem where data is stored among different computers or agents that seek to…

Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…

Lasso, or $\ell^1$ regularized least squares, has been explored extensively for its remarkable sparsity properties. It is shown in this paper that the solution to Lasso, in addition to its sparsity, has robustness properties: it is the…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $\ell_{1,\infty}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression…

Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…

Sparsity is a fundamental modeling principle in statistics, signal processing, and data science. However, optimization with sparsity constraints is notoriously difficult. We introduce a new convex relaxation framework for {sparse…

Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…