Related papers: Decoupling Shrinkage and Selection for the Bayesia…
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…
Modern approaches to perform Bayesian variable selection rely mostly on the use of shrinkage priors. That said, an ideal shrinkage prior should be adaptive to different signal levels, ensuring that small effects are ruled out, while keeping…
Selecting a subset of variables for linear models remains an active area of research. This paper reviews many of the recent contributions to the Bayesian model selection and shrinkage prior literature. A posterior variable selection summary…
Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models but, at the same time, introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a…
We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…
We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…
We introduce a Bayesian framework for mixed-type multivariate regression using continuous shrinkage priors. Our framework enables joint analysis of mixed continuous and discrete outcomes and facilitates variable selection from the $p$…
There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…
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…
The paper addresses joint sparsity selection in the regression coefficient matrix and the error precision (inverse covariance) matrix for high-dimensional multivariate regression models in the Bayesian paradigm. The selected sparsity…
Quantile regression is a powerful data analysis tool that accommodates heterogeneous covariate-response relationships. We find that by coupling the asymmetric Laplace working likelihood with appropriate shrinkage priors, we can deliver…
Sparse regression based on global-local shrinkage priors are increasingly used for Bayesian modeling of modern high-dimensional data, but scaling up the Gibbs sampler for posterior inference remains a challenge. While much effort has gone…
Compressing large-scale neural networks is essential for deploying models on resource-constrained devices. Most existing methods adopt weight pruning or low-bit quantization individually, often resulting in suboptimal compression rates to…
We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…
Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly…
In this article, we propose a simple method to perform variable selection as a post model-fitting exercise using continuous shrinkage priors such as the popular horseshoe prior. The proposed Signal Adaptive Variable Selector (SAVS) approach…
Currently several Bayesian approaches are available to estimate large sparse precision matrices, including Bayesian graphical Lasso (Wang, 2012), Bayesian structure learning (Banerjee and Ghosal, 2015), and graphical horseshoe (Li et al.,…
Crossing of fitted conditional quantiles is a prevalent problem for quantile regression models. We propose a new Bayesian modelling framework that penalises multiple quantile regression functions toward the desired non-crossing space. We…
Network complexity and computational efficiency have become increasingly significant aspects of deep learning. Sparse deep learning addresses these challenges by recovering a sparse representation of the underlying target function by…
We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically…