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Finite mixture models have been widely used for the modelling and analysis ofdata from heterogeneous populations. Maximum likelihood estimation of theparameters is typically carried out via the Expectation-Maximization (EM)algorithm. The complexity of the implementation of the algorithm depends on theparametric distribution that is adopted as the component densities of themixture model. In the case of the skew normal and skew t-distributions, forexample, the E-step would involve complicated expressions that arecomputationally expensive to evaluate. This can become quite time-consuming forlarge and/or high-dimensional datasets. In this paper, we develop amultithreaded version of the EM algorithm for the fitting of finite mixturemodels. Due to the structure of the algorithm for these models, the E- andM-steps can be easily reformulated to be executed in parallel across multiplethreads to take advantage of the processing power available in modern-daymulticore machines. Our approach is simple and easy to implement, requiringonly small changes to standard code. To illustrate the approach, we focus on afairly general mixture model that includes as special or limiting cases some ofthe most commonly used mixture models including the normal, t-, skew normal,and skew t-mixture models.

A simple multithreaded implementation of the EM algorithm for mixture models