Generalized Beta Mixtures of Gaussians

Details Generalized Beta Mixtures of Gaussians Generalized Beta Mixtures of Gaussians

2011-07-25

arxiv.org/abs/1107.4976v2

Statistics

Methodology

Advances in Neural Information Processing Systems 24 edited by J. Shawe-Taylor and R.S. Zemel and P. Bartlett and F. Pereira a

Scientific paper

In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. We first propose a new class of normal scale mixtures through a novel generalized beta distribution that encompasses many interesting priors as special cases. This encompassing framework should prove useful in comparing competing priors, considering properties and revealing close connections. We then develop a class of variational Bayes approximations through the new hierarchy presented that will scale more efficiently to the types of truly massive data sets that are now encountered routinely.

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