Related papers: Analysis of Basis Pursuit Via Capacity Sets

It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. The goal is to recover the…

Matching pursuits are a class of greedy algorithms commonly used in signal processing, for solving the sparse approximation problem. They rely on an atom selection step that requires the calculation of numerous projections, which can be…

Traditional machine learning methods usually minimize a simple loss function to learn a predictive model, and then use a complex performance measure to measure the prediction performance. However, minimizing a simple loss function cannot…

Although modern deep learning often relies on massive over-parameterized models, the fundamental interplay between capacity, sparsity, and robustness in low-capacity networks remains a vital area of study. We introduce a controlled…

We propose a probe for the analysis of deep learning architectures that is based on machine learning and approximation theoretical principles. Given a deep learning architecture and a training set, during or after training, the Sparsity…

In this paper, we propose sparsity-aware data-selective adaptive filtering algorithms with adjustable penalties. Prior work incorporates a penalty function into the cost function used in the optimization that originates the algorithms to…

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training,…

This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…

We show that sparsity constrained optimization problems over low dimensional spaces tend to have a small duality gap. We use the Shapley-Folkman theorem to derive both data-driven bounds on the duality gap, and an efficient primalization…

Suppose we have a signal y which we wish to represent using a linear combination of a number of basis atoms a_i, y=sum_i x_i a_i = Ax. The problem of finding the minimum L0 norm representation for y is a hard problem. The Basis Pursuit (BP)…

This paper proposes an adaptive near-field beam training method to enhance performance in multi-user and multipath environments. The approach identifies multiple strongest beams through beam sweeping and linearly combines their received…

The problem of finding the maximum likelihood estimates for the regression coefficients in generalised linear models with an L1 sparsity penalty is shown to be equivalent to minimising the unpenalised maximum log-likelihood function over a…

Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set…

Supercomputers are equipped with an increasingly large number of cores to use computational power as a way of solving problems that are otherwise intractable. Unfortunately, getting serial algorithms to run in parallel to take advantage of…

Inspired by alternating direction method of multipliers and the idea of operator splitting, we propose a efficient algorithm for solving large-scale quadratically constrained basis pursuit. Experimental results show that the proposed…

We present a theoretical analysis of the average performance of OMP for sparse approximation. For signals that are generated from a dictionary with $K$ atoms and coherence $\mu$ and coefficients corresponding to a geometric sequence with…

Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved $\ell_0$ norm. In this paper, a special type of tensor complementarity problems with…

Greedy Pursuits are very popular in Compressed Sensing for sparse signal recovery. Though many of the Greedy Pursuits possess elegant theoretical guarantees for performance, it is well known that their performance depends on the statistical…

Let $X=(x_1,...,x_n)$ be a random vector that satisfies a weak small ball property and whose coordinates $x_i$ satisfy that $\|x_i\|_{L_p} \lesssim \sqrt{p} \|x_i\|_{L_2}$ for $p \sim \log n$. In \cite{LM_compressed}, it was shown that $N$…

Recent work has shown that deep learning models in NLP are highly sensitive to low-level correlations between simple features and specific output labels, leading to overfitting and lack of generalization. To mitigate this problem, a common…