We study a mean-field spike and slab variational Bayes (VB) approximation to
Bayesian model selection priors in sparse high-dimensional linear regression.
Under compatibility conditions on the design matrix, oracle inequalities are
derived for the mean-field VB approximation, implying that it converges to the
sparse truth at the optimal rate and gives optimal prediction of the response
vector. The empirical performance of our algorithm is studied, showing that it
works comparably well as other state-of-the-art Bayesian variable selection
methods. We also numerically demonstrate that the widely used coordinate-ascent
variational inference (CAVI) algorithm can be highly sensitive to the parameter
updating order, leading to potentially poor performance. To mitigate this, we
propose a novel prioritized updating scheme that uses a data-driven updating
order and performs better in simulations. The variational algorithm is
implemented in the R package 'sparsevb'.

研究了高维稀疏线性回归中，贝叶斯模型选择先验的平均场斯派克和板块变分贝叶斯（VB）逼近，证明在设计矩阵兼容条件下，该逼近方式渐进地达到最优稀疏性真理和响应向量的最优预测，经实验证明该算法与其他最先进的贝叶斯变量选择方法具有相当的性能，同时提出了一种新的优先更新方案来提高变分推理算法的性能。