标题： 自适应脊选择器 (ARiS) 显示英文标题

标题： Adaptive Ridge Selector (ARiS)

摘要： 我们引入了一种新的线性模型收缩变量选择算子，称为 ARiS（\emph{自适应岭选择器}）。 该方法受到 RVM（\emph{相关向量机}）的启发，RVM 使用贝叶斯分层线性设定来进行变量选择和模型估计。 通过扩展 RVM 算法，我们在回归系数精度上引入了一个适当的先验分布$v_{j}^{-1} \sim f(v_{j}^{-1}|\eta)$，其中$\eta$是一个标量超参数。 采用利用完整后验条件分布的新拟合方法来最大化联合后验分布$p(\boldsymbol\beta,\sigma^{2},\mathbf{v}^{-1}|\mathbf{y},\eta)$，在超参数$\eta$的值已知的情况下。 提出了一种经验贝叶斯方法来选择$\eta$。 这种方法与其他正则化最小二乘估计器（包括 Lasso 及其变体、非负套索和普通岭回归）进行了对比。 通过各种模拟数据实例探讨了性能差异。 结果显示，在稀疏设置下预测和模型选择的准确性更高，并且随着样本量的增加，模型选择的准确性有了显著提高。 显示英文摘要

摘要： We introduce a new shrinkage variable selection operator for linear models which we term the \emph{adaptive ridge selector} (ARiS). This approach is inspired by the \emph{relevance vector machine} (RVM), which uses a Bayesian hierarchical linear setup to do variable selection and model estimation. Extending the RVM algorithm, we include a proper prior distribution for the precisions of the regression coefficients, $v_{j}^{-1} \sim f(v_{j}^{-1}|\eta)$, where $\eta$ is a scalar hyperparameter. A novel fitting approach which utilizes the full set of posterior conditional distributions is applied to maximize the joint posterior distribution $p(\boldsymbol\beta,\sigma^{2},\mathbf{v}^{-1}|\mathbf{y},\eta)$ given the value of the hyper-parameter $\eta$. An empirical Bayes method is proposed for choosing $\eta$. This approach is contrasted with other regularized least squares estimators including the lasso, its variants, nonnegative garrote and ordinary ridge regression. Performance differences are explored for various simulated data examples. Results indicate superior prediction and model selection accuracy under sparse setups and drastic improvement in accuracy of model choice with increasing sample size.