Bootstrap estimation and model selection for multivariate normal mixtures using parallel computing with graphics processing units

In applications of multivariate finite mixture models, estimating the number of unknown components is often difficult. We propose a bootstrap information criterion, whereby we calculate the expected log-likelihood at maximum a posteriori estimates for model selection. Accurate estimation using the bootstrap requires a large number of bootstrap replicates. We accelerate this computation by employing parallel processing with graphics processing units (GPUs) on the Compute Unified Device Architecture (CUDA) platform. We conducted a runtime comparison of CUDA algorithms between implementation on the GPU and that on a CPU. The results showed significant performance gains in the proposed CUDA algorithms over multithread CPUs.