Related papers: Sparse Bayesian Lasso via a Variable-Coefficient $…
Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on…
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…
Due to its self-regularizing nature and its ability to quantify uncertainty, the Bayesian approach has achieved excellent recovery performance across a wide range of sparse signal recovery applications. However, most existing methods are…
Sparse penalized quantile regression provides an effective framework for variable selection and robust estimation in high-dimensional data analysis. When ex planatory variables are organized into groups, achieving sparsity both within and…
The Lasso is biased. Concave penalized least squares estimation (PLSE) takes advantage of signal strength to reduce this bias, leading to sharper error bounds in prediction, coefficient estimation and variable selection. For prediction and…
Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…
Feature selection is one of the most decisive tools in understanding data and machine learning models. Among other methods, sparsity induced by $L^{1}$ penalty is one of the simplest and best studied approaches to this problem. Although…
We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is…
Sparse manifold learning algorithms combine techniques in manifold learning and sparse optimization to learn features that could be utilized for downstream tasks. The standard setting of compressive sensing can not be immediately applied to…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…
In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is…
One of the crucial tasks in many inference problems is the extraction of sparse information out of a given number of high-dimensional measurements. In machine learning, this is frequently achieved using, as a penality term, the $L_p$ norm…
We consider penalized regression models under a unified framework where the particular method is determined by the form of the penalty term. We propose a fully Bayesian approach that incorporates both sparse and dense settings and show how…
We consider a problem of estimating a sparse group of sparse normal mean vectors. The proposed approach is based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their…
In longitudinal study, it is common that response and covariate are not measured at the same time, which complicates the analysis to a large extent. In this paper, we take into account the estimation of generalized varying coefficient model…
This work is a re-examination of the sparse Bayesian learning (SBL) of linear regression models of Tipping (2001) in a high-dimensional setting. We propose a hard-thresholded version of the SBL estimator that achieves, for orthogonal design…
Motivated by the observation that a given signal $\boldsymbol{x}$ admits sparse representations in multiple dictionaries $\boldsymbol{\Psi}_d$ but with varying levels of sparsity across dictionaries, we propose two new algorithms for the…
When a series of (related) linear models has to be estimated it is often appropriate to combine the different data-sets to construct more efficient estimators. We use $\ell_1$-penalized estimators like the Lasso or the Adaptive Lasso which…
We propose a general algorithmic framework for Bayesian model selection. A spike-and-slab Laplacian prior is introduced to model the underlying structural assumption. Using the notion of effective resistance, we derive an EM-type algorithm…