455 research outputs found
A Tutorial on Bayesian Nonparametric Models
A key problem in statistical modeling is model selection, how to choose a
model at an appropriate level of complexity. This problem appears in many
settings, most prominently in choosing the number ofclusters in mixture models
or the number of factors in factor analysis. In this tutorial we describe
Bayesian nonparametric methods, a class of methods that side-steps this issue
by allowing the data to determine the complexity of the model. This tutorial is
a high-level introduction to Bayesian nonparametric methods and contains
several examples of their application.Comment: 28 pages, 8 figure
Convergence of latent mixing measures in finite and infinite mixture models
This paper studies convergence behavior of latent mixing measures that arise
in finite and infinite mixture models, using transportation distances (i.e.,
Wasserstein metrics). The relationship between Wasserstein distances on the
space of mixing measures and f-divergence functionals such as Hellinger and
Kullback-Leibler distances on the space of mixture distributions is
investigated in detail using various identifiability conditions. Convergence in
Wasserstein metrics for discrete measures implies convergence of individual
atoms that provide support for the measures, thereby providing a natural
interpretation of convergence of clusters in clustering applications where
mixture models are typically employed. Convergence rates of posterior
distributions for latent mixing measures are established, for both finite
mixtures of multivariate distributions and infinite mixtures based on the
Dirichlet process.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1065 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
- …