# The Bayesian Lasso

@article{Park2008TheBL, title={The Bayesian Lasso}, author={Trevor H Park and George Casella}, journal={Journal of the American Statistical Association}, year={2008}, volume={103}, pages={681 - 686} }

The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters have independent Laplace (i.e., double-exponential) priors. Gibbs sampling from this posterior is possible using an expanded hierarchy with conjugate normal priors for the regression parameters and independent exponential priors on their variances. A connection with the inverse-Gaussian distribution provides tractable full conditional distributions. The…

## 2,484 Citations

Bayesian lasso regression

- Computer Science
- 2009

New aspects of the broader Bayesian treatment of lasso regression are introduced, and it is shown that the standard lasso prediction method does not necessarily agree with model-based, Bayesian predictions.

A New Bayesian Lasso.

- Computer ScienceStatistics and its interface
- 2014

This paper considers a fully Bayesian treatment that leads to a new Gibbs sampler with tractable full conditional posterior distributions and shows that the new algorithm has good mixing property and performs comparably to the existing Bayesian method in terms of both prediction accuracy and variable selection.

Priors on the Variance in Sparse Bayesian Learning; the demi-Bayesian Lasso

- Computer Science
- 2008

This work outlines simple modifications of existing algorithms to solve this new variant which essentially uses type-II maximum likelihood to fit the Bayesian Lasso model and proposes an Elastic-net heuristic to help with modeling correlated inputs.

Approximate Gibbs sampler for Bayesian Huberized lasso

- Computer Science
- 2022

A new posterior computation algorithm for the Bayesian Huberized lasso regression is proposed based on the approximation of full conditional distribution and it is possible to estimate a tuning parameter for robustness of the pseudo-Huber loss function.

Sparsity via new Bayesian Lasso

- Computer Science
- 2020

This paper proposed Scale Mixture of Normals mixing with Rayleigh density on their variances to represent the double exponential distribution and proposed Hierarchical model formulation presented with Gibbs sampler under SMNR as alternative Bayesian analysis of minimization problem of classical lasso.

Sparse modifying algorithm in Bayesian lasso

- Computer Science
- 2014

In the present pape4 the authors propase aiL erncient algorithm which modifies the Bayesian lasso estimates so as to be sparse, to investigate the ernciency of the proposed aLgorithm.

High-Dimensional Bayesian Regularised Regression with the BayesReg Package

- Computer Science, Mathematics
- 2016

This paper introduces bayesreg, a new toolbox for fitting Bayesian penalized regression models with continuous shrinkage prior densities, and features Bayesian linear regression with Gaussian or heavy-tailed error models and Bayesian logistic regression with ridge, lasso, horseshoes and horseshoe estimators.

Robust Bayesian Regularized Estimation Based on Regression Model

- Computer Science, Mathematics
- 2015

A new robust coefficient estimation and variable selection method based on Bayesian adaptive Lasso regression, developed based on the Bayesian hierarchical model framework, where the distribution is treated as a mixture of normal and gamma distributions and put different penalization parameters for different regression coefficients.

Sparse Bayesian linear regression using generalized normal priors

- Computer Science, MathematicsInt. J. Wavelets Multiresolution Inf. Process.
- 2017

A sparse Bayesian linear regression model is proposed that generalizes the Bayesian Lasso to a class of Bayesian models with scale mixtures of normal distributions as priors for the regression…

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