Expanding the Computation of Mixture Models by the use of Hermite Polynomials and Ideals

Abstract

Mixture models have found uses in many areas. To list a few: unsupervised learning, empirical Bayes, latent class and trait models. The current applications of mixture models to empirical data is limited to computing a mixture model from the same parametric family, e.g. Gaussians or Poissons. In this paper it is shown that by using Hermite polynomials and ideals, the modeling of a mixture process can be extended to include different families in terms of their cumulative distribution functions (cdfs)

The use of algebraic geometry to the solution of the mixture problem expands the application of algebra to statistics. The algebraic method used is a well known. It is its application to statistics that is different