Sub-optimality of some continuous shrinkage priors

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• 作者：Anirban Bhattacharya^a ; David B. Dunson^b ; Debdeep Pati^c ; Natesh S. Pillai^d ; ^{pillai@fas.harvard.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Bayesian ; Convergence rate ; High dimensional ; Lasso ; ℓ_1ℓ1 ; Lower bound ; Penalized regression ; Regularization ; Shrinkage prior ; Sub-optimal
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：126
• 期：12
• 页码：3828-3842
• 全文大小：322 K

文摘

Two-component mixture priors provide a traditional way to induce sparsity in high-dimensional Bayes models. However, several aspects of such a prior, including computational complexities in high-dimensions, interpretation of exact zeros and non-sparse posterior summaries under standard loss functions, have motivated an amazing variety of continuous shrinkage priors, which can be expressed as global–local scale mixtures of Gaussians. Interestingly, we demonstrate that many commonly used shrinkage priors, including the Bayesian Lasso, do not have adequate posterior concentration in high-dimensional settings.