arXiv research

In this paper, we study a simple iterative method for finding the Dantzig selector, which was designed for linear regression problems. The method consists of two main stages. The first stage is to approximate the Dantzig selector through a fixed-point formulation of solutions to the Dantzig selector problem. The second…

New method solves large-scale linear programming problems for sparse signal reconstruction.

Paper analyzes structured matrix recovery using generalized Dantzig selector.

A new Dantzig Selector with an optimal denoising matrix for reinforcement learning.

Enhanced Dantzig selector reduces recovery error in high dimensions.

In many applications one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to the challenge, in a compressive sensing framework, one is given only an undersampl…

We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and residuals. Motivated by the significant advances in integer optimization over the…

New method aggregates GDS analyses of randomly selected interaction models to identify important factors in screening experiments.

A new method estimates high-dimensional multi-response models with structured parameters.

We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS…

LSTD is a popular algorithm for value function approximation. Whenever the number of features is larger than the number of samples, it must be paired with some form of regularization. In particular, L1-regularization methods tend to perform feature selection by promoting sparsity, and thus, are well-suited for high-dim…

We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the $\ell_{2}$-prediction error and the $\ell_{1}$-risk of the lasso and the Dantzig selector are optimal up to an explicit multiplicative constant. Thus we can estimate a high-dim…

In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible to adopt recent developments in saddle-point optimization, to achieve the optim…

Study on estimating sparse transition matrix of partially-observed VAR with noisy and sparse data.

In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated measurements on both the design and dependent variables may be leveraged to enhance a spa…

To estimate a sparse linear model from data with Gaussian noise, consilience from lasso and compressed sensing literatures is that thresholding estimators like lasso and the Dantzig selector have the ability in some situations to identify with high probability part of the significant covariates asymptotically, and are …

We tackle estimation and confidence intervals in high-dimensional regression with missing covariates.

Popular sparse estimation methods based on $\ell_1$-relaxation, such as the Lasso and the Dantzig selector, require the knowledge of the variance of the noise in order to properly tune the regularization parameter. This constitutes a major obstacle in applying these methods in several frameworks---such as time series, …

Suppose that we observe $y \in \mathbb{R}^f$ and $X \in \mathbb{R}^{f \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 β^* + ε\\ X & = & X_0 + W \end{eqnarray*} where $X_0$ is a $f \times m$ design matrix with independent subgaussian row vectors, $ε\in \mathbb{R}^f$ is a noise vector…

In this paper, we study a fast approximation method for {\it large-scale high-dimensional} sparse least-squares regression problem by exploiting the Johnson-Lindenstrauss (JL) transforms, which embed a set of high-dimensional vectors into a low-dimensional space. In particular, we propose to apply the JL transforms to …

A new R package for high-dimensional regression and precision matrix estimation.

Guarantees recovery of compressible signals from adversarial noise.

Iterative algorithms are ubiquitous in the field of data mining. Widely known examples of such algorithms are the least mean square algorithm, backpropagation algorithm of neural networks. Our contribution in this paper is an improvement upon this iterative algorithms in terms of their respective performance metrics an…

In this paper, we consider low rank matrix estimation using either matrix-version Dantzig Selector $\hat{A}_λ^d$ or matrix-version LASSO estimator $\hat{A}_λ^L$. We consider sub-Gaussian measurements, $i.e.$, the measurements $X_1,\ldots,X_n\in\mathbb{R}^{m\times m}$ have $i.i.d.$ sub-Gaussian entries. Suppose $\textrm…

Paper presents a new method for solving sparse learning problems.

A fast method estimates stability of ensemble feature selectors.

New conditions ensure Dantzig-Wolfe relaxation matches rank-constrained optimization problems.

This paper improves CS algorithms for high SNR consistency.

Defines spectral selectors on lens spaces for contactomorphisms.

The study proves properties of spectral selectors for contact manifolds and applies them to contact big fibers and geodesics.

An action selector associates, in a suitable way, to each compactly supported Hamiltonian on a symplectic manifold an action value of the Hamiltonian. Action selectors are known to exist for a broad class of symplectic manifolds. We show how the existence of an action selector leads to sharp energy capacity inequalitie…

Study compares penalized regression methods for high-dimensional data.

This paper improves bandwidth selectors for SPBNs to enhance their performance.

T-Rex selector selects variables fast and controls FDR in high-dimensional data.

ASAC uses actor-critic models to optimize observation selection in medical settings.

Study non-squeezing phenomena in contact geometry using specific capacities.

Meta-algorithm selection aims to choose the best algorithm selector for a given problem instance.

Estimates quantum system states using Pauli measurements with improved convergence rates.

We explore the performance of several automatic bandwidth selectors, originally designed for density gradient estimation, as data-based procedures for nonparametric, modal clustering. The key tool to obtain a clustering from density gradient estimators is the mean shift algorithm, which allows to obtain a partition not…

Develops a test for comparing linear models without assuming sparsity.

SLR tackles sparse linear regression problems, showing hardness for efficient algorithms.

ESAC improves reinforcement learning by lookahead and intuition.

New method learns to encode predictions within interpretations, improving evaluation.

RODE learns roles to simplify multi-agent tasks.

An algorithm reduces breast cancer detection data complexity using effect sizes.

Prototype selection improved using topological data analysis.

Framework improves text classification under budget constraints.

IEN speeds up T-Rex+GVS for fast, efficient GWAS.