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Hierarchical Bayesian nonparametric models with applications (2010)
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@MISC{Teh10hierarchicalbayesian,
author = {Yee Whye Teh and Michael I. Jordan},
title = {Hierarchical Bayesian nonparametric models with applications},
year = {2010}
}
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Abstract
Hierarchical modeling is a fundamental concept in Bayesian statistics. The basic idea is that parameters are endowed with distributions which may themselves introduce new parameters, and this construction recurses. In this review we discuss the role of hierarchical modeling in Bayesian nonparametrics, focusing on models in which the infinite-dimensional parameters are treated hierarchically. For example, we consider a model in which the base measure for a Dirichlet process is itself treated as a draw from another Dirichlet process. This yields a natural recursion that we refer to as a hierarchical Dirichlet process. We also discuss hierarchies based on the Pitman-Yor process and on completely random processes. We demonstrate the value of these hierarchical constructions in a wide range of practical applications, in problems in computational biology, computer vision and natural language processing. 1
Keyphrases
hierarchical bayesian nonparametric model dirichlet process hierarchical modeling random process new parameter base measure practical application computational biology pitman-yor process fundamental concept infinite-dimensional parameter hierarchical dirichlet process computer vision wide range basic idea natural language processing natural recursion hierarchical construction bayesian statistic bayesian nonparametrics
