Mixture Models: Building a Parameter Space

TL;DR

This paper introduces a novel geometric representation of mixture model parameter spaces, enabling better interpretability and computational efficiency for mixtures of exponential families.

Contribution

It proposes a new geometric framework for representing identifiable mixture model parameters, improving interpretability and computational tractability.

Findings

Parameter space representation becomes more tractable and interpretable.

The geometric structure facilitates faster algorithms for mixture models.

Applicable to general mixtures of exponential families.

Abstract

Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for general mixtures of exponential families, where the parameters are identifiable, interpretable, and, due to a tractable geometric structure, the space allows fast computational algorithms to be constructed.