Related papers: Adaptive Shrinkage with a Nonparametric Bayesian L…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
We introduce a new empirical Bayes approach for large-scale multiple linear regression. Our approach combines two key ideas: (i) the use of flexible "adaptive shrinkage" priors, which approximate the nonparametric family of scale mixture of…
Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…
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…
We study the problem of variable selection in convex nonparametric least squares (CNLS). Whereas the least absolute shrinkage and selection operator (Lasso) is a popular technique for least squares, its variable selection performance is…
Bayesian fused lasso is one of the sparse Bayesian methods, which shrinks both regression coefficients and their successive differences simultaneously. In this paper, we propose a Bayesian fused lasso modeling via horseshoe prior. By…
Prior distributions for high-dimensional linear regression require specifying a joint distribution for the unobserved regression coefficients, which is inherently difficult. We instead propose a new class of shrinkage priors for linear…
We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and…
Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…
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…
Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome $Y$ to a large number of covariates $\mathbf {X}$, for example,…
The lasso and elastic net linear regression models impose a double-exponential prior distribution on the model parameters to achieve regression shrinkage and variable selection, allowing the inference of robust models from large data sets.…
This paper introduces a novel Bayesian approach for variable selection in high-dimensional and potentially sparse regression settings. Our method replaces the indicator variables in the traditional spike and slab prior with continuous,…
We introduce a new class of distributions named log-adjusted shrinkage priors for the analysis of sparse signals, which extends the three parameter beta priors by multiplying an additional log-term to their densities. The proposed prior has…
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…
There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ($p>>n$) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating…
In the past decade, many Bayesian shrinkage models have been developed for linear regression problems where the number of covariates, $p$, is large. Computing the intractable posterior are often done with three-block Gibbs samplers (3BG),…
Neural networks are the cornerstone of modern machine learning, yet can be difficult to interpret, give overconfident predictions and are vulnerable to adversarial attacks. Bayesian neural networks (BNNs) provide some alleviation of these…
We introduce BLAST, Bayesian Linear regression with Adaptive Shrinkage for Transfer, a Bayesian multi-source transfer learning framework for high-dimensional linear regression. The proposed analytical framework leverages global-local…
In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…