Optimal transport for vector Gaussian mixture models

Finite mixture models can describe a wide range of statistical phenomena. They have been successfully applied to numerous fields including biology, economics, engineering, and social sciences [15]. The first major use and analysis of mixture models is perhaps due to the mathematician and biostatistician Karl Pearson over 120 years ago who explicitly decomposed a distribution into two normal distributions for characterizing non-normal attributes of forehead to body length ratios in female shore crab populations [16]. The literature on analyzing and applying mixture models is growing due to their simplicity, versatility and flexibility. One of the most commonly used mixture models is the Gaussian mixture model (GMM), which is a weighted sum of Gaussian distributions.