Bayesian lasso regression

By Chris Hans. 2009

501 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0a3873992669e8577a906149a81007cb13c70599

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Citations in the corpus

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).”
Asymptotic Properties of Bayes Risk of a General Class of Shrinkage Priors in Multiple Hypothesis Testing Under Sparsity (2013, methodology): “Some early examples of one-group shrinkage priors are the t-prior (Tipping (2001)), the Laplace prior in the context of Bayesian Lasso (Park and Casella (2008) and Hans (2009)) and the family of normal–exponential–gamma priors (Griffin and Brown (2005)).”
Diagnosing and correcting the effects of multicollinearity: Bayesian implications of ridge regression (2019, background): “A similar 167 idea is the Bayesian lasso regression (Park and Casella, 2008, Hans, 2009).”
Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective (2014, methodology): “The last five years have seen tremendous activity in this area, beginning with the work of Park and Casella [2008] and Hans [2009] with the introduction of a Bayesian analogue of the lasso [Tibshirani, 1996] based on the choice of inverse-gamma densities for π(λ(2)j ), leading to Laplace priors on β”
Elastic Net Regression Modeling With the Orthant Normal Prior (2011, methodology): “Regression modeling under the double-exponential prior and connections with the lasso have drawn recent interest (e.g., Park and Casella 2008; Hans 2009).”
Foundations of Linear and Generalized Linear Models (2015, methodology): “Park and Casella (2007) and Hans (2009) used this result as a mechanism for point and interval estimation of {βj}.”
Generalized Beta Mixtures of Gaussians (2011, background): “For example, it is well known that Gaussian priors induce `2 penalties, while double exponential priors induce `1 penalties [8, 19, 13, 1].”
Asymptotic Properties of Bayes Risk for the Horseshoe Prior (2013, methodology): “Park and Casella (2008); Hans (2009); Li and Goel (2006)), our method of proof fails to show any contraction property for the double exponential prior.”
BAYESIAN LINEAR REGRESSION WITH SPARSE PRIORS (2014, background): “, [14, 23, 24]) can cope with somewhat higher dimensions, but truly high-dimensional models are out of reach of fully Bayesian methods at the present time.”
Local shrinkage rules, Lévy processes and regularized regression (2010, methodology): “…work has been motivated by problems in high dimensional regularized regression, where we observe data y =Xβ +ε and wish to estimate β. 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.”
Bayesian Model and Dimension Reduction for Uncertainty Propagation: Applications in Random Media (2017, methodology): “Several sparsity enforcing approaches were tested in this work, including the Laplacian prior (or LASSO regression [71, 26]) as well as Student-t type prior models [45, 55, 22].”
The Bayesian elastic net (2010, background): “The Bayesian lasso ( bl ) (Park and Casella 2008; Hans 2009a,b) not only gives the interval estimation but also provided the posterior distribution for the lasso estimator. bl assigns a double exponential prior on β , which is essentially a scale mixture of normals where the mixing is through an…”
On the half-cauchy prior for a global scale parameter (2011, methodology): “For example, choosing an exponential prior for each u(2)i results in a Laplace prior, used in the Bayesian lasso model (Park and Casella 2008; Hans 2009). This class of models provides a Bayesian alternative to penalized-likelihood estimation. When the underlying vector of means is sparse, these glo”
Machine Learning Advances for Time Series Forecasting (2020, methodology): “The LASSO replaces the Gaussian prior by a Laplace prior (Hans, 2009; Park & Casella, 2008).”
Text as Data (2017, background): “For example, ridge regression maximizes the posterior under independent Gaussian priors on each coefficient, while Park and Casella (2008) and Hans (2009) give Bayesian interpretations to the lasso.”