相关论文: Coordinate Descent for MCP/SCAD Penalized Least Sq…

A number of variable selection methods have been proposed involving nonconvex penalty functions. These methods, which include the smoothly clipped absolute deviation (SCAD) penalty and the minimax concave penalty (MCP), have been…

Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…

We develop randomized (block) coordinate descent (CD) methods for linearly constrained convex optimization. Unlike most CD methods, we do not assume the constraints to be separable, but let them be coupled linearly. To our knowledge, ours…

Novel coordinate descent (CD) methods are proposed for minimizing nonconvex functions consisting of three terms: (i) a continuously differentiable term, (ii) a simple convex term, and (iii) a concave and continuous term. First, by extending…

We consider approaches for improving the efficiency of algorithms for fitting nonconvex penalized regression models such as SCAD and MCP in high dimensions. In particular, we develop rules for discarding variables during cyclic coordinate…

We consider a class of structured fractional minimization problems, in which the numerator part of the objective is the sum of a differentiable convex function and a convex non-smooth function, while the denominator part is a convex or…

$\ell_1$ penalized quantile regression is used in many fields as an alternative to penalized least squares regressions for high-dimensional data analysis. Existing algorithms for penalized quantile regression either use linear programming,…

In compressed sensing, the l0-norm minimization of sparse signal reconstruction is NP-hard. Recent work shows that compared with the best convex relaxation (l1-norm), nonconvex penalties can better approximate the l0-norm and can…

Sparse signal recovery from under-determined systems presents significant challenges when using conventional L_0 and L_1 penalties, primarily due to computational complexity and estimation bias. This paper introduces a truncated Huber…

In this paper we consider sparse approximation problems, that is, general $l_0$ minimization problems with the $l_0$-"norm" of a vector being a part of constraints or objective function. In particular, we first study the first-order…

By the asymptotic oracle property, non-convex penalties represented by minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) have attracted much attentions in high-dimensional data analysis, and have been widely used…

In recent studies on sparse modeling, $l_q$ ($0<q<1$) regularization has received considerable attention due to its superiorities on sparsity-inducing and bias reduction over the $l_1$ regularization.In this paper, we propose a cyclic…

Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has…

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding…

Coordinate descent algorithms are widely used in machine learning and large-scale data analysis due to their strong optimality guarantees and impressive empirical performance in solving non-convex problems. In this work, we introduce Block…

In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…

In this paper, we bring together two trends that have recently emerged in sparse signal recovery: the problem of sparse signals that stem from finite alphabets and the techniques that introduce concave penalties. Specifically, we show that…

We investigate the signal reconstruction performance of sparse linear regression in the presence of noise when piecewise continuous nonconvex penalties are used. Among such penalties, we focus on the SCAD penalty. The contributions of this…

Block-coordinate descent (BCD) is the method of choice to solve numerous large scale optimization problems, however their theoretical study for non-convex optimization, has received less attention. In this paper, we present a new…

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…