102 research outputs found
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
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