A fast approximate fitting for mixture of multivariate skew t-distribution via EM algorithm

A mixture of multivariate canonical fundamental skew t-distribution (CFUST) has been of interest in various fields. In particular, interest in the unsupervised learning society is noteworthy. However, fitting the model via EM algorithm suffers from significant processing time. The main cause is due to the calculation of many multivariate t-cdfs (cumulative distribution functions) in E-step. In this article, we provide an approximate, but fast calculation method for the in univariate fashion, which is the product of successively conditional univariate t-cdfs with Taylor's first order approximation. By replacing all multivariate t-cdfs in E-step with the proposed approximate versions, we obtain the admissible results of fitting the model, where it gives 85% reduction time for the 5 dimensional skewness case of the Australian Institution Sport data set. For this approach, discussions about rough properties, advantages and limits are also presented.