Related papers: Sparse Estimation with Strongly Correlated Variabl…
In the Multiple Measurements Vector (MMV) model, measurement vectors are connected to unknown, jointly sparse signal vectors through a linear regression model employing a single known measurement matrix (or dictionary). Typically, the…
High covariate dimensionality is increasingly occurrent in model estimation, and existing techniques to address this issue typically require sparsity or discrete heterogeneity of the \emph{unobservable} parameter vector. However, neither…
Accurate uncertainty quantification is critical for reliable predictive modeling. Existing methods typically address either aleatoric uncertainty due to measurement noise or epistemic uncertainty resulting from limited data, but not both in…
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…
High-dimensional inference methods often rely on coefficient sparsity, an assumption that can be restrictive when signals are dense but individually weak. In such settings, valid inference may still be possible if the covariates exhibit…
This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…
We address the exact recovery of a k-sparse vector in the noiseless setting when some partial information on the support is available. This partial information takes the form of either a subset of the true support or an approximate subset…
We consider the problem of selecting covariates in spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and,…
Variable selection methods are required in practical statistical modeling, to identify and include only the most relevant predictors, and then improving model interpretability. Such variable selection methods are typically employed in…
Accurately estimating the proportion of true signals among a large number of variables is crucial for enhancing the precision and reliability of scientific research. Traditional signal proportion estimators often assume independence among…
Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…
We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features.…
While K-means is known to be a standard clustering algorithm, its performance may be compromised due to the presence of outliers and high-dimensional noisy variables. This paper proposes adaptively robust and sparse K-means clustering…
Recently, $L_1$ regularization have been attracted extensive attention and successfully applied in mean-variance portfolio selection for promoting out-of-sample properties and decreasing transaction costs. However, $L_1$ regularization…
For Gaussian sampling matrices, we provide bounds on the minimal number of measurements $m$ required to achieve robust weighted sparse recovery guarantees in terms of how well a given prior model for the sparsity support aligns with the…
Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…
Subspace clustering refers to the problem of clustering high-dimensional data that lie in a union of low-dimensional subspaces. State-of-the-art subspace clustering methods are based on the idea of expressing each data point as a linear…
Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in…
Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…
We study the problem of recovering the underlining sparse signals from clean or noisy phaseless measurements. Due to the sparse prior of signals, we adopt an L0regularized variational model to ensure only a small number of nonzero elements…