Related papers: Bayesian High-dimensional Linear Regression with S…
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…
We consider Bayesian variable selection in sparse high-dimensional regression, where the number of covariates $p$ may be large relative to the samples size $n$, but at most a moderate number $q$ of covariates are active. Specifically, we…
We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…
This work considers variational Bayesian inference as an inexpensive and scalable alternative to a fully Bayesian approach in the context of sparsity-promoting priors. In particular, the priors considered arise from scale mixtures of Normal…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
We review recent results for high-dimensional sparse linear regression in the practical case of unknown variance. Different sparsity settings are covered, including coordinate-sparsity, group-sparsity and variation-sparsity. The emphasis is…
Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are…
The emergence of Big Data raises the question of how to model economic relations when there is a large number of possible explanatory variables. We revisit the issue by comparing the possibility of using dense or sparse models in a Bayesian…
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…
For the important classical problem of inference on a sparse high-dimensional normal mean vector, we propose a novel empirical Bayes model that admits a posterior distribution with desirable properties under mild conditions. In particular,…
Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of…
In this work, we focus on variational Bayesian inference on the sparse Deep Neural Network (DNN) modeled under a class of spike-and-slab priors. Given a pre-specified sparse DNN structure, the corresponding variational posterior contraction…
Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold standard method for Bayesian sparse linear regression [CPS09,…
Recently, a number of mostly $\ell_1$-norm regularized least squares type deterministic algorithms have been proposed to address the problem of \emph{sparse} adaptive signal estimation and system identification. From a Bayesian perspective,…
Two key challenges in modern statistical applications are the large amount of information recorded per individual, and that such data are often not collected all at once but in batches. These batch effects can be complex, causing…
In this paper, we introduce a new sparsity-promoting prior, namely, the "normal product" prior, and develop an efficient algorithm for sparse signal recovery under the Bayesian framework. The normal product distribution is the distribution…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
This article is about estimation and inference methods for high dimensional sparse (HDS) regression models in econometrics. High dimensional sparse models arise in situations where many regressors (or series terms) are available and the…