Related papers: Support driven reweighted $\ell_1$ minimization

We study the properties of sparse reconstruction of transformed $\ell_1$ (TL1) minimization and present improved theoretical results about the recoverability and the accuracy of this reconstruction from undersampled measurements. We then…

The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed…

In recent years, stochastic gradient descent (SGD) methods and randomized linear algebra (RLA) algorithms have been applied to many large-scale problems in machine learning and data analysis. We aim to bridge the gap between these two…

In this paper, we consider a class of non-convex and non-smooth sparse optimization problems, which encompass most existing nonconvex sparsity-inducing terms. We show the second-order optimality conditions only depend on the nonzeros of the…

We study the problem of exact support recovery based on noisy observations and present Refined Least Squares (RLS). Given a set of noisy measurement $$ \myvec{y} = \myvec{X}\myvec{\theta}^* + \myvec{\omega},$$ and $\myvec{X} \in…

Sparsity is one of the key concepts that allows the recovery of signals that are subsampled at a rate significantly lower than required by the Nyquist-Shannon sampling theorem. Our proposed framework uses arbitrary multiscale transforms,…

We study constrained reinforcement learning (CRL) from a novel perspective by setting constraints directly on state density functions, rather than the value functions considered by previous works. State density has a clear physical and…

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…

In recent years, semi-supervised learning (SSL) has gained significant attention due to its ability to leverage both labeled and unlabeled data to improve model performance, especially when labeled data is scarce. However, most current SSL…

We consider the problem of finding an approximate solution to $\ell_1$ regression while only observing a small number of labels. Given an $n \times d$ unlabeled data matrix $X$, we must choose a small set of $m \ll n$ rows to observe the…

Sample inefficiency is a long-lasting challenge in deep reinforcement learning (DRL). Despite dramatic improvements have been made, the problem is far from being solved and is especially challenging in environments with sparse or delayed…

Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…

The wavelet frame systems have been playing an active role in image restoration and many other image processing fields over the past decades, owing to the good capability of sparsely approximating piece-wise smooth functions such as images.…

Reinforcement learning (RL) is gaining attention by more and more researchers in quantitative finance as the agent-environment interaction framework is aligned with decision making process in many business problems. Most of the current…

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…

This paper proposes a distributed weighted regularized least squares algorithm (DWRLS) based on spherical radial basis functions and spherical quadrature rules to tackle spherical data that are stored across numerous local servers and…

To recover a sparse signal from an underdetermined system, we often solve a constrained L1-norm minimization problem. In many cases, the signal sparsity and the recovery performance can be further improved by replacing the L1 norm with a…

Upside Down Reinforcement Learning (UDRL) is a promising framework for solving reinforcement learning problems which focuses on learning command-conditioned policies. In this work, we extend UDRL to the task of learning a…

The integration of distributed energy resources (DER) has escalated the challenge of voltage magnitude regulation in distribution networks. Traditional model-based approaches, which rely on complex sequential mathematical formulations,…

We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the…