Dependent Random Partitions by Shrinking Toward an Anchor
arxiv(2023)
摘要
Although exchangeable processes from Bayesian nonparametrics have been used
as a generating mechanism for random partition models, we deviate from this
paradigm to explicitly incorporate clustering information in the formulation
our random partition model. Our shrinkage partition distribution takes any
partition distribution and shrinks its probability mass toward an anchor
partition. We show how this provides a framework to model
hierarchically-dependent and temporally-dependent random partitions. The
shrinkage parameters control the degree of dependence, accommodating at its
extremes both independence and complete equality. Since a priori knowledge of
items may vary, our formulation allows the degree of shrinkage toward the
anchor to be item-specific. Our random partition model has a tractable
normalizing constant which allows for standard Markov chain Monte Carlo
algorithms for posterior sampling. We prove intuitive theoretical properties
for our distribution and compare it to related partition distributions. We show
that our model provides better out-of-sample fit in a real data application.
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