Related papers: Pattern recovery by SLOPE

Sparse Subspace Clustering (SSC) is a popular unsupervised machine learning method for clustering data lying close to an unknown union of low-dimensional linear subspaces; a problem with numerous applications in pattern recognition and…

This paper explores the homogeneity of coefficients in high-dimensional regression, which extends the sparsity concept and is more general and suitable for many applications. Homogeneity arises when one expects regression coefficients…

Generalized linear and additive models are very efficient regression tools but the selection of relevant terms becomes difficult if higher order interactions are needed. In contrast, tree-based methods also known as recursive partitioning…

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…

We consider the performance of a least-squares regression model, as judged by out-of-sample $R^2$. Shapley values give a fair attribution of the performance of a model to its input features, taking into account interdependencies between…

We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…

We consider a high-dimensional multi-outcome regression in which $q,$ possibly dependent, binary and continuous outcomes are regressed onto $p$ covariates. We model the observed outcome vector as a partially observed latent realization from…

Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to be estimated. Recently there emerges a few…

In this paper, we consider the recovery of block sparse signals, whose nonzero entries appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from incomplete linear measurement. A high order sufficient…

The two primary approaches for high-dimensional regression problems are sparse methods (e.g., best subset selection, which uses the L0-norm in the penalty) and ensemble methods (e.g., random forests). Although sparse methods typically yield…

This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of…

Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…

Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…

This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…

Is it possible to find the sparsest vector (direction) in a generic subspace $\mathcal{S} \subseteq \mathbb{R}^p$ with $\mathrm{dim}(\mathcal{S})= n < p$? This problem can be considered a homogeneous variant of the sparse recovery problem,…

Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…

Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a given dictionary. This paper resorts to exponential…

Since sparse neural networks usually contain many zero weights, these unnecessary network connections can potentially be eliminated without degrading network performance. Therefore, well-designed sparse neural networks have the potential to…

We consider the linear regression problem. We propose the S-Lasso procedure to estimate the unknown regression parameters. This estimator enjoys sparsity of the representation while taking into account correlation between successive…

We study the problem of recovering a known cluster structure in a sparse network, also known as the planted partitioning problem, by means of statistical mechanics. We find a sharp transition from un-recoverable to recoverable structure as…