An Approximated Collapsed Variational Bayes Approach to Variable Selection in Linear Regression
提出一种近似折叠变分贝叶斯算法用于线性回归的模型选择，该算法在典型假设下能以指数速率包含真实变量，计算速度比马尔可夫链蒙特卡洛快一个数量级。
In this work, we propose a novel approximated collapsed variational Bayes approach to model selection in linear regression. The approximated collapsed variational Bayes algorithm offers improvements over mean field variational Bayes by marginalizing over a subset of parameters and using mean field variational Bayes over the remaining parameters in an analogous fashion to collapsed Gibbs sampling. We have shown that the proposed algorithm, under typical regularity assumptions, (a) includes variables in the true underlying model at an exponential rate in the sample size, or (b) excludes the variables at least at the first order rate in the sample size if the variables are not in the true model. Simulation studies show that the performance of the proposed method is close to that of a particular Markov chain Monte Carlo sampler and a path search based variational Bayes algorithm, but requires an order of magnitude less time. The proposed method is also highly competitive with penalized methods, expectation propagation, stepwise AIC/BIC, BMS, and EMVS under various settings. Supplementary materials for the article are available online.