Optimal transport for Gaussian mixture models

IEEE Access. 2018:7:6269-6278. doi: 10.1109/ACCESS.2018.2889838. Epub 2018 Dec 27.

Abstract

We introduce an optimal mass transport framework on the space of Gaussian mixture models. These models are widely used in statistical inference. Specifically, we treat Gaussian mixture models as a submanifold of probability densities equipped with the Wasserstein metric. The topology induced by optimal transport is highly desirable and natural because, in contrast to total variation and other metrics, the Wasserstein metric is weakly continuous (i.e., convergence is equivalent to convergence of moments). Thus, our approach provides natural ways to compare, interpolate and average Gaussian mixture models. Moreover, the approach has low computational complexity. Different aspects of the framework are discussed and examples are presented for illustration purposes.

Keywords: Gaussian mixture models; Wasserstein metric; optimal mass transport; statistical signal analysis.