1 research outputs found
Minimum message length estimation of mixtures of multivariate Gaussian and von Mises-Fisher distributions
Mixture modelling involves explaining some observed evidence using a
combination of probability distributions. The crux of the problem is the
inference of an optimal number of mixture components and their corresponding
parameters. This paper discusses unsupervised learning of mixture models using
the Bayesian Minimum Message Length (MML) criterion. To demonstrate the
effectiveness of search and inference of mixture parameters using the proposed
approach, we select two key probability distributions, each handling
fundamentally different types of data: the multivariate Gaussian distribution
to address mixture modelling of data distributed in Euclidean space, and the
multivariate von Mises-Fisher (vMF) distribution to address mixture modelling
of directional data distributed on a unit hypersphere. The key contributions of
this paper, in addition to the general search and inference methodology,
include the derivation of MML expressions for encoding the data using
multivariate Gaussian and von Mises-Fisher distributions, and the analytical
derivation of the MML estimates of the parameters of the two distributions. Our
approach is tested on simulated and real world data sets. For instance, we
infer vMF mixtures that concisely explain experimentally determined
three-dimensional protein conformations, providing an effective null model
description of protein structures that is central to many inference problems in
structural bioinformatics. The experimental results demonstrate that the
performance of our proposed search and inference method along with the encoding
schemes improve on the state of the art mixture modelling techniques.Comment: 46 page