|
Abstract:
|
For under high dimensional linear regression analysis, variable selection (VS) is very helpful. Bayesian variable selection (BVS) methods is both useful and flexible. To determine the posterior is the most important part. However, MCMC becomes slow or intractable when the dimensionality is sufficiently large. For this reason, alternatives including Variational Bayes (VB) have been developed. In VS scenario, application of VB gives VBVS. One popular method of VBVS is to update the regression coefficients element-wise. It is computationally fast. But the literature has shown that it may accumulate errors during the optimization process, and it's sensitive to correlation between the predictors. An alternative is to update all regression coefficients jointly, yielding a batch-wise algorithm. However, it involves large matrix inversion, which may be inaccurate. We propose a cluster-wise VBVS procedure. In the first step, we identify the clusters within the predictors by empirical correlation matrix. In the second step, we apply VBVS to these clusters sequentially. Data examples show cluster-wise VBVS outperforms or ties with its competitors.
|
