The Bayesian Lasso

By Trevor Park, George Casella. 2008

3,276 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Estimation Considerations in Contextual Bandits (2017, methodology): “In Appendix C, we provide a Bayesian way of using LASSO estimation in a Thompson sampling or UCB contextual bandit motivated by [48].”
Bayesian group factor analysis with structured sparsity (2016, background): “In contrast, an 1 penalty corresponds to double exponential or Laplace priors, also known as the Bayesian Lasso (Tibshirani, 1996; Park and Casella, 2008; Hans, 2009).”
Penalized regression, standard errors, and Bayesian lassos (2010, methodology): “In the Bayesian framework, Park and Casella (2008) suggested some alternatives based on empirical Bayes using marginal maximum likelihood, putting λ1 or λ2 into the Gibbs sampler with an appropriate hyperprior. In this paper, we use the suggested gamma prior for a proper posterior from Park and Case”
A review of Bayesian variable selection methods: what, how and which (2009, methodology): “The random effect variant of the method, where μ is a parameter and has its own prior, is better known as the Bayesian Lasso (Park and Casella 2008; Yi and Xu 2008).”
Sparse Variational Analysis of Linear Mixed Models for Large Data Sets. (2011, background): “A few examples of these are Tipping (2001); Bishop and Tipping (2000); Figueiredo (2003); Park and Casella (2008).”
A Model-Averaging Approach for High-Dimensional Regression (2014, methodology): “These include the lasso method (Tibshirani 1996; Zou, Hastie, and Tibshirani 2007) and its variants (Yuan and Lin 2006; Zou 2006), Bayesian lasso (Park and Casella 2008), least-angle regression (Efron et al. 2004), elastic net (Zou and Hastie 2005), the smoothly clipped absolute deviation penalty…”
Efficient posterior sampling for high-dimensional imbalanced logistic regression. (2019, background): “Another common prior is the double exponential prior, also known as the Laplace prior [30, 24].”
Genomic Selection in Plant Breeding: A Comparison of Models (2012, background): “In the case of the BL (Park and Casella, 2008; Yi and Xu, 2008; de los Campos et al., 2009), the shrinkage is marker specifi c and dependent on a regularization parameter λ.”
Small Sample Size Solutions (2020, methodology): “For example, specifying double-exponential prior distributions for the regression coefficients will result in posterior modes that are the same as the classical lasso estimates (Park & Casella, 2008).”
Evaluation of Genomic Prediction Methods for Fusarium Head Blight Resistance in Wheat (2012, methodology): “…GS models tested were ridge regression (RR) BLUP (Meuwissen et al., 2001; Whittaker et al., 2000), Bayesian LASSO (BL) (de los Campos et al., 2009b; Park and Casella, 2008), reproducing kernel Hilbert spaces (RKHS) (Gianola et al., 2006) regression, and random forest (RF) (Breiman, 2001)…”
Geometric ergodicity of the Bayesian lasso (2013, methodology): “Park and Casella [14] consider a Bayesian treatment of this model with a Laplace/Inverse-Gamma prior on (β, σ).”
Local shrinkage rules, Lévy processes and regularized regression (2010, methodology): “Good examples of recent Bayesian research in this area are Park and Casella (2008) and Hans (2009), who explored Bayesian versions of the traditional lasso penalty.”
Scalable Variational Inference for Bayesian Variable Selection in Regression, and Its Accuracy in Genetic Association Studies (2012, background): “The variational inference procedure we describe does not exploit the sparsity of the prior, so it may be possible to extend it to non-sparse priors that induce shrinkage in the regression coefficients, including normal-gamma priors (Griffin and Brown 2010) and the Bayesian Lasso (Park and Casella 20”
Testing for Granger Causality in Large Mixed-Frequency VARs (2016, neutral): “distribution (Park and Casella, 2008).”
Differentially Private Bayesian Inference for Exponential Families (2018, methodology): “We seek a tractable form for the full conditional of s under the normal approximation, which is the product of a normal density and a Laplace density: A similar situation arises in the Bayesian Lasso [22], and we will employ the same variable augmentation trick.”