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An Alternative Prior Process for Nonparametric Bayesian Clustering
Hanna Wallach, Shane Jensen, Lee Dicker and Katherine Heller
In: AISTATS 2010, Sardinia, Italy(2010).
AbstractPrior distributions play a crucial role in
Bayesian approaches to clustering. Two
commonly-used prior distributions are the
Dirichlet and Pitman-Yor processes. In this
paper, we investigate the predictive probabilities
that underlie these processes, and the
implicit \rich-get-richer" characteristic of the
resulting partitions. We explore an alternative
prior for nonparametric Bayesian clustering,
the uniform process, for applications
where the \rich-get-richer" property is undesirable.
We also explore the cost of this new
process: partitions are no longer exchangeable
with respect to the ordering of variables.
We present new asymptotic and simulationbased
results for the clustering characteristics
of the uniform process and compare
these with known results for the Dirichlet
and Pitman-Yor processes. Finally, we compare
performance on a real-world document
clustering task, demonstrating the practical
advantage of the uniform process despite its
lack of exchangeability over orderings. [Edit]
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