
Convergence of latent mixing measures in finite and infinite mixture models
This paper studies convergence behavior of latent mixing measures that a...
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On the Identifiability of Finite Mixtures of Finite Product Measures
The problem of identifiability of finite mixtures of finite product meas...
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Identifiability and optimal rates of convergence for parameters of multiple types in finite mixtures
This paper studies identifiability and convergence behaviors for paramet...
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On the geometric properties of finite mixture models
In this paper we relate the geometry of extremal points to properties of...
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On posterior contraction of parameters and interpretability in Bayesian mixture modeling
We study posterior contraction behaviors for parameters of interest in t...
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Deconvolution of dust mixtures by latent Dirichlet allocation in forensic science
Dust particles recovered from the soles of shoes may be indicative of th...
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Dirichlet Process Mixtures of Order Statistics with Applications to Retail Analytics
The rise of "big data" has led to the frequent need to process and store...
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Convergence of de Finetti's mixing measure in latent structure models for observed exchangeable sequences
Mixtures of product distributions are a powerful device for learning about heterogeneity within data populations. In this class of latent structure models, de Finetti's mixing measure plays the central role for describing the uncertainty about the latent parameters representing heterogeneity. In this paper posterior contraction theorems for de Finetti's mixing measure arising from finite mixtures of product distributions will be established, under the setting the number of exchangeable sequences of observed variables increases while sequence length(s) may be either fixed or varied. The role of both the number of sequences and the sequence lengths will be carefully examined. In order to obtain concrete rates of convergence, a firstorder identifiability theory for finite mixture models and a family of sharp inverse bounds for mixtures of product distributions will be developed via a harmonic analysis of such latent structure models. This theory is applicable to broad classes of probability kernels composing the mixture model of product distributions for both continuous and discrete domain. Examples of interest include the case the probability kernel is only weakly identifiable in the sense of Ho and Nguyen (2016), the case where the kernel is itself a mixture distribution as in hierarchical models, and the case the kernel may not have a density with respect to a dominating measure on an abstract domain such as Dirichlet processes.
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