相关论文: A Novel Sparse Regularizer

We introduce a novel scheme for choosing the regularization parameter in high-dimensional linear regression with Lasso. This scheme, inspired by Lepski's method for bandwidth selection in non-parametric regression, is equipped with both…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

We present a method for supervised learning of sparsity-promoting regularizers for image denoising. Sparsity-promoting regularization is a key ingredient in solving modern image reconstruction problems; however, the operators underlying…

We propose a general framework of iteratively reweighted l1 methods for solving lp regularization problems. We prove that after some iteration k, the iterates generated by the proposed methods have the same support and sign as the limit…

We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…

In this paper, we consider the joint task of simultaneously optimizing (i) the weights of a deep neural network, (ii) the number of neurons for each hidden layer, and (iii) the subset of active input features (i.e., feature selection).…

There have been many attempts to identify high-dimensional network features via multivariate approaches. Specifically, when the number of voxels or nodes, denoted as p, are substantially larger than the number of images, denoted as n, it…

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…

A low precision deep neural network training technique for producing sparse, ternary neural networks is presented. The technique incorporates hard- ware implementation costs during training to achieve significant model compression for…

Nonlocal image representation or group sparsity has attracted considerable interest in various low-level vision tasks and has led to several state-of-the-art image denoising techniques, such as BM3D, LSSC. In the past, convex optimization…

Deep Neural Networks have demonstrated remarkable success in various domains but remain susceptible to adversarial examples, which are slightly altered inputs designed to induce misclassification. While adversarial attacks typically…

We present algorithms for efficiently learning regularizers that improve generalization. Our approach is based on the insight that regularizers can be viewed as upper bounds on the generalization gap, and that reducing the slack in the…

Plug-and-Play (PnP) algorithms are a class of iterative algorithms that address image inverse problems by combining a physical model and a deep neural network for regularization. Even if they produce impressive image restoration results,…

Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This…

A central goal of neuroscience is to understand how activity in the nervous system is related to features of the external world, or to features of the nervous system itself. A common approach is to model neural responses as a weighted…

This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics…

This paper investigates the theoretical guarantees of L1-analysis regularization when solving linear inverse problems. Most of previous works in the literature have mainly focused on the sparse synthesis prior where the sparsity is measured…

Sparse optimization has seen its advances in recent decades. For scenarios where the true sparsity is unknown, regularization turns out to be a promising solution. Two popular non-convex regularizations are the so-called $L_0$ norm and…

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…

Noiseless compressive sensing is a two-steps setting that allows for undersampling a sparse signal and then reconstructing it without loss of information. The LASSO algorithm, based on $\lone$ regularization, provides an efficient and…