Mixtures of Multivariate Power Exponential Distributions

TL;DR

This paper introduces a flexible family of mixture models based on multivariate power exponential distributions, capable of modeling data with varying tail heaviness and peakedness, with efficient algorithms for parameter estimation.

Contribution

It proposes a new family of parsimonious mixture models using eigen-decomposition and develops a generalized EM algorithm combining convex optimization and line search techniques.

Findings

Models effectively capture heavy tails and skewness in data.

Algorithm demonstrates good convergence on toy and benchmark datasets.

Flexible modeling of complex data distributions is achieved.

Abstract

An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness has received much attention in the model-based clustering literature recently, we investigate the use of a distribution that can deal with both varying tail-weight and peakedness of data. A family of parsimonious models is proposed using an eigen-decomposition of the scale matrix. A generalized expectation-maximization algorithm is presented that combines convex optimization via a minorization-maximization approach and optimization based on accelerated line search algorithms on the Stiefel manifold. Lastly, the utility of this family of models is illustrated using both toy and benchmark data.