Divide and Conquer Algorithm of Bayesian Density Estimation

• Activity Number: 176 - Bayesian Mixture Modeling, Clustering and Unsupervised Learning
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ya Su*
• Companies: University of Kentucky

Abstract

Data sets for statistical analysis become wildly large even with some difficulty of storing on one single machine. Even when the data can be stored in one machine, the computational cost would still be intimidating. We propose a divide and conquer solution to density estimation using Bayesian mixture model including the infinite mixture case. The methodology can be generalized to other application problems where Bayesian mixture model is adopted. The proposed prior on each machine or subsample modifies the original prior on both mixing probabilities as well as other components on the rest of parameters in the distributions being mixed. The ultimate estimator is obtained by taking the average of posterior samples corresponding to the proposed prior on each subsets. Despite the tremendous speed bump thanks to data splitting, the posterior contraction rate of the proposed method stays the same (up to a log factor) as if the data is analyzed as a whole. One of our simulations is performed in a shape constrained deconvolution context and reveals promising results. The application to a GWAS data set reveals the advantage over some naive method.