Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective

By By P. Richard Hahn, Carlos M. Carvalho. 2014

170 citations recorded by the source corpus.

Selecting a subset of variables for linear models remains an active area of research. This article reviews many of the recent contributions to the Bayesian model selection and shrinkage prior literature. A posterior variable selection summary is proposed, which distills a full posterior distribution over regression coefficients into a sequence of sparse linear predictors.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a3dba6e4b636bfeb942a9db29c195bf7cb4433b3

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Citations in the corpus

Heterogeneous Treatment Effects in Digital Experimentation (2014, methodology): “Hahn and Carvalho (2014) survey this type of sparse decision-theoretic posterior summary in the context of prediction loss and provide a specific ‘decoupled shrinkage and selection’ (DSS) algorithm that targets minimization of L0 penalized squared-error loss. Specific to our case, we are focused on ”
A Nonparametric Bayesian Analysis of Heterogenous Treatment Effects in Digital Experimentation (2014, background): “stic ^ in the L 2 norm when moving from loss to expected loss. With the ‘optimal’ magnitude of the L 0 penalty, , likely unknown or undeﬁned, we will minimize (25) over a path of interesting values. Hahn and Carvalho (2014) survey this type of sparse decision-theoretic posterior summary in the conte”
Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion) (2020, unknown): “Moreover, such Bayesian “fit-the-fit” posterior summarization strategies can be formalized from a decision theoretic perspective (Sivaganesan et al., 2017; Hahn and Carvalho, 2015); we do not explore this possibility further here.”
The Median Probability Model and Correlated Variables (2018, methodology): “An example of one possible approach is given in [13], who suggest running a lasso regression of Xβ̄ onto X.”
Bayesian Regression Using a Prior on the Model Fit: The R2-D2 Shrinkage Prior (2016, methodology): “posed the penalized credible region variable selection method, which ts the full model under a continuous shrinkage prior, and then selects the sparsest solution within the posterior credible region. Hahn and Carvalho (2015) proposed the decoupling shrinkage and selection method, which uses a loss f”