标题： 一种分层贝叶斯框架用于构建稀疏性诱导先验 显示英文标题

标题： A Hierarchical Bayesian Framework for Constructing Sparsity-inducing Priors

摘要： 变量选择技术由于涉及高维数据的回归和分类应用的增加而越来越受到统计学家的青睐，在这些应用中我们期望一些预测变量是不重要的。 在这种情况下，涉及模型后验分布的马尔可夫链蒙特卡罗探索的贝叶斯变量选择技术可能计算成本过高，因此人们关注了诸如使用诱导估计稀疏性的先验的最大后验（MAP）估计等准贝叶斯方法。 我们专注于后者，扩展至今提出的一些层次结构，以提供对最先进的惩罚优化方法的贝叶斯解释和推广，并同时提供一种自然的方式将关于参数的先验信息纳入该框架。 我们给出了如何使用此层次结构计算线性回归和逻辑回归的MAP估计以及高斯图模型中的稀疏精度矩阵估计的例子。 此外，还利用该框架推导出了一种自适应组Lasso方法。 显示英文摘要

摘要： Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant. In this context, Bayesian variable selection techniques involving Markov chain Monte Carlo exploration of the posterior distribution over models can be prohibitively computationally expensive and so there has been attention paid to quasi-Bayesian approaches such as maximum a posteriori (MAP) estimation using priors that induce sparsity in such estimates. We focus on this latter approach, expanding on the hierarchies proposed to date to provide a Bayesian interpretation and generalization of state-of-the-art penalized optimization approaches and providing simultaneously a natural way to include prior information about parameters within this framework. We give examples of how to use this hierarchy to compute MAP estimates for linear and logistic regression as well as sparse precision-matrix estimates in Gaussian graphical models. In addition, an adaptive group lasso method is derived using the framework.