Generalized Beta Mixtures of Gaussians
Generalized Beta Mixtures of Gaussians
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发表时间：
2011-07
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通讯作者：
Artin Armagan;D. Dunson;M. Clyde
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作者：
Artin Armagan;D. Dunson;M. Clyde
近年来，人们提出了各种各样的收缩先验，它们在解决大规模回归问题方面具有巨大的前景。一般来说，这些新的先验可以表示为正态的尺度混合，但比传统的柯西和双指数先验具有更复杂的形式和更好的性质。我们首先通过一种新颖的广义贝塔分布提出一类新的正态尺度混合物，其中包含许多有趣的先验作为特殊情况。这个包罗万象的框架在比较竞争先验、考虑属性和揭示密切联系方面应该是有用的。然后，我们通过提出的新层次结构开发一类变分贝叶斯近似，它将更有效地扩展到现在经常遇到的真正海量数据集的类型。
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.