Related papers: A Proximal-Gradient Homotopy Method for the Sparse…
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…
In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\ell_0$ pseudo norm…
The problems of Lasso regression and optimal design of experiments share a critical property: their optimal solutions are typically \emph{sparse}, i.e., only a small fraction of the optimal variables are non-zero. Therefore, the…
Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…
We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as…
This paper develops a novel Continuous-time Accelerated Proximal Point Algorithm (CAPPA) for $\ell_1$-minimization problems with provable fixed-time convergence guarantees. The problem of $\ell_1$-minimization appears in several contexts,…
We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discrete signed measures and enable…
The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…
Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
We propose a new algorithm for the problem of recovering data that adheres to multiple, heterogeneous low-dimensional structures from linear observations. Focusing on data matrices that are simultaneously row-sparse and low-rank, we propose…
This paper considers stochastic convex optimization problems with smooth functional constraints arising in constrained estimation and robust signal recovery. We operate in the high-dimensional and highly-constrained setting, where oracle…
We present improved sampling complexity bounds for stable and robust sparse recovery in compressed sensing. Our unified analysis based on l1 minimization encompasses the case where (i) the measurements are block-structured samples in order…
Hard thresholding pursuit (HTP) is a recently proposed iterative sparse recovery algorithm which is a result of combination of a support selection step from iterated hard thresholding (IHT) and an estimation step from the orthogonal…
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…
Stochastic second-order methods achieve fast local convergence in strongly convex optimization by using noisy Hessian estimates to precondition the gradient. However, these methods typically reach superlinear convergence only when the…
Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from…
In this paper the efficiency of multilevel sparse tensor approximation methods for high-dimensional affine parametric diffusion equations is investigated. Methodologically, the recently presented Sparse Alternating Least Squares (SALS)…
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…
In this paper, we propose a new greedy algorithm for sparse approximation, called SLS for Single L_1 Selection. SLS essentially consists of a greedy forward strategy, where the selection rule of a new component at each iteration is based on…