Bayesian Variable Selection in Linear Regression

By T. Mitchell, J. Beauchamp. 1988

Subfields: Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

The State of Sparsity in Deep Neural Networks (2019, background): “Interestingly, Louizos et al. (2017b) showed that their ob-jective function under the l 0 penalty is a special case of a variational lower-bound over the parameters of the network under a spike and slab (Mitchell & Beauchamp, 1988) prior.”
Learning Sparse Neural Networks through L0 Regularization (2017, background): “3 is in fact a special case of a variational bound over the parameters involving spike and slab (Mitchell & Beauchamp, 1988) priors and approximate posteriors; we refer interested readers to appendix A.”
Bayesian Compression for Deep Learning (2017, background): “One example of the aforementioned framework is the spike-and-slab distribution [50], the golden standard for sparse Bayesian inference.”
Large-Scale Feature Learning With Spike-and-Slab Sparse Coding (2012, background): “The notion of a spike-and-slab prior was established in statistics by Mitchell and Beauchamp (1988). Outside the context of unsupervised feature discovery for supervised learning, the basic form of the S3C model (i.”
Bayesian group factor analysis with structured sparsity (2016, methodology): “The canonical Bayesian sparsity-inducing prior is the spike-and-slab prior, which is a mixture of a point mass at zero and a flat distribution across the space of real values, often modeled as a Gaussian with a large variance term (Mitchell and Beauchamp, 1988; West, 2003).”
The Practical Implementation of Bayesian Model Selection (2001, background): “It should also be mentioned that in one the first Bayesian variable selection treatments of the setup (3.8), Mitchell and Beauchamp (1988) proposed spike-and-slab priors.”
Generalized Beta Mixtures of Gaussians (2011, methodology): “An alternative and widely applied Bayesian framework relies on variable selection priors and Bayesian model selection/averaging [18, 9, 16, 15].”
Bayesian inference of chemical kinetic models from proposed reactions (2015, methodology): “We impose point-mass mixture priors on the rate constants of all proposed elementary reactions and use an adaptive Markov chain Monte Carlo (MCMC) method to efficiently explore the model space, along with the rate parameter values (Ji and Schmidler, 2013; Mitchell and Beauchamp, 1988).”
Bayesian Wavelet Regression on Curves With Application to a Spectroscopic Calibration Problem (2001, methodology): “Brown, Vannucci, and Fearn 1998a, b) we explored Bayesian approaches to the problem of selecting predictor variables in this multivariate regression context.”
Learning Feature Selection Dependencies in Multi-task Learning (2013, methodology): “The sparsity assumption can be introduced by carrying out Bayesian inference under a sparsity enforcing prior for the model coefficients [2, 3], or by minimizing a loss function penalized by some sparse regularizer [4, 5].”
Minimal Penalties for Gaussian Model Selection (2007, methodology): “A Bayesian point of view appears in George and Foster [17] using hierarchical Bayesian models introduced by Mitchell and Beauchamp [32].”
Posterior Computation with the Gibbs Zig-Zag Sampler (2020, background): “A popular shrinkage prior is the spike-and-slab prior (Mitchell and Beauchamp, 1988; Ishwaran and Rao, 2005), which is a mixture of a spike at zero and a higher variance component.”