相关论文: Trust-Region Methods for Sparse Relaxation

This paper considers an explicit continuation method and the trust-region updating strategy for the unconstrained optimization problem. Moreover, in order to improve its computational efficiency and robustness, the new method uses the…

Sparse reconstruction approaches using the re-weighted l1-penalty have been shown, both empirically and theoretically, to provide a significant improvement in recovering sparse signals in comparison to the l1-relaxation. However, numerical…

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…

Stochastic variational inference allows for fast posterior inference in complex Bayesian models. However, the algorithm is prone to local optima which can make the quality of the posterior approximation sensitive to the choice of…

We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed…

In this paper, we consider the sparse least squares regression problem with probabilistic simplex constraint. Due to the probabilistic simplex constraint, one could not apply the L1 regularization to the considered regression model. To find…

In this paper, we study a few challenging theoretical and numerical issues on the well known trust region policy optimization for deep reinforcement learning. The goal is to find a policy that maximizes the total expected reward when the…

Mean field theory has provided theoretical insights into various algorithms by letting the problem size tend to infinity. We argue that the applications of mean-field theory go beyond theoretical insights as it can inspire the design of…

Sparse representation can be described in high dimensions and used in many applications, including MRI imaging and radar imaging. In some cases, methods have been proposed to solve the high-dimensional sparse representation problem, but…

Many image processing applications benefited remarkably from the theory of sparsity. One model of sparsity is the cosparse analysis one. It was shown that using l_1-minimization one might stably recover a cosparse signal from a small set of…

The l1/l2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the…

We investigate a trust-region algorithm to solve a nonconvex optimization problem with $L^p$-regularization for $p\in(0,1)$. The algorithm relies on descent properties of a so-called generalized Cauchy point that can be obtained efficiently…

Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…

In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…

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…

Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…

There are a large number of methods for solving under-determined linear inverse problem. Many of them have very high time complexity for large datasets. We propose a new method called Two-Stage Sparse Representation (TSSR) to tackle this…

In this work, we consider solving optimization problems with a stochastic objective and deterministic equality constraints. We propose a Trust-Region Sequential Quadratic Programming method to find both first- and second-order stationary…

The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…

We propose a communicationally and computationally efficient algorithm for high-dimensional distributed sparse learning. At each iteration, local machines compute the gradient on local data and the master machine solves one shifted $l_1$…