Related papers: Sparse Identification and Estimation of Large-Scal…
We propose a new algorithm for sparse estimation of eigenvectors in generalized eigenvalue problems (GEP). The GEP arises in a number of modern data-analytic situations and statistical methods, including principal component analysis (PCA),…
We investigate methods for penalized regression in the presence of missing observations. This paper introduces a method for estimating the parameters which compensates for the missing observations. We first, derive an unbiased estimator of…
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…
Remote sensing change detection aims to localize and characterize scene changes between two time points and is central to applications such as environmental monitoring and disaster assessment. Meanwhile, visual autoregressive models (VARs)…
Modern statistical learning algorithms are capable of amazing flexibility, but struggle with interpretability. One possible solution is sparsity: making inference such that many of the parameters are estimated as being identically 0, which…
The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
This study introduces Variational Automatic Relevance Determination (VARD), a novel approach tailored for fitting sparse additive regression models in high-dimensional settings. VARD distinguishes itself by its ability to independently…
Time-varying systems are a challenge in many scientific and engineering areas. Usually, estimation of time-varying parameters or signals must be performed online, which calls for the development of responsive online algorithms. In this…
We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…
Parameter estimation and the variable selection are two pioneer issues in regression analysis. While traditional variable selection methods require prior estimation of the model parameters, the penalized methods simultaneously carry on…
We discuss the fundamental issue of identification in linear instrumental variable (IV) models with unknown IV validity. With the assumption of the "sparsest rule", which is equivalent to the plurality rule but becomes operational in…
Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…
In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…
Relevance vector machine (RVM) is a popular sparse Bayesian learning model typically used for prediction. Recently it has been shown that improper priors assumed on multiple penalty parameters in RVM may lead to an improper posterior.…
We propose a regularized factor-augmented vector autoregressive (FAVAR) model that allows for sparsity in the factor loadings. In this framework, factors may only load on a subset of variables which simplifies the factor identification and…
Robust estimators for linear regression require non-convex objective functions to shield against adverse affects of outliers. This non-convexity brings challenges, particularly when combined with penalization in high-dimensional settings.…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in…