Distributed Bayesian posterior voting strategy for massive data

The emergence of massive data has driven recent interest in developing statistical learning and large-scale algorithms for analysis on distributed platforms. One of the widely used statistical approaches is split-and-conquer (SaC), which was originally performed by aggregating all local solutions through a simple average to reduce the computational burden caused by communication costs. Aiming at lower computation cost and satisfactorily acceptable accuracy, this paper extends SaC to Bayesian variable selection for ultra-high dimensional linear regression and builds BVSaC for aggregation. Suppose ultrahigh-dimensional data are stored in a distributed manner across multiple computing nodes, with each computing resource containing a disjoint subset of data. On each node machine, we perform variable selection and coefficient estimation through a hierarchical Bayes formulation. Then, a weighted majority voting method BVSaC is used to combine the local results to retain good performance. The proposed approach only requires a small portion of computation cost on each local dataset and therefore eases the computational burden, especially in Bayesian computation, meanwhile, pays a little cost to receive accuracy, which in turn increases the feasibility of analyzing extraordinarily large datasets. Simulations and a real-world example show that the proposed approach performed as well as the whole sample hierarchical Bayes method in terms of the accuracy of variable selection and estimation.