Estimation and inference for the Wasserstein distance between mixing measures in topic models

Understand

The Wasserstein distance between mixing measures has come to occupy a central place in the statistical analysis of mixture models.

• This work proposes a new canonical interpretation of this distance and provides tools to perform inference on the Wasserstein distance between mixing measures in topic models.
• We consider the general setting of an identifiable mixture model consisting of mixtures of distributions from a set $\mathcal{A}$ equipped with an arbitrary metric $d$, and show that the Wasserstein distance between mixing measures is uniquely characterized as the most discriminative convex extension of the metric $d$ to the set of mixtures of elements of $\mathcal{A}$.
• The Wasserstein distance between mixing measures has been widely used in the study of such models, but without axiomatic justification.