Dependent Random Partitions by Shrinking Toward an Anchor
提出一种新的随机划分模型，通过向锚点划分收缩概率质量来显式纳入聚类信息，支持层次依赖和时间依赖的划分，并允许项目特定的收缩程度，后验采样可通过标准MCMC算法实现。
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 of our random partition model. Our shrinkage partition distribution takes any partition distribution and shrinks its probability mass toward a specific anchor partition. We show how this provides a framework to model hierarchically-dependent and temporally-dependent random partitions. The shrinkage parameter controls the degree of dependence, accommodating at its extremes both independence and complete equality. Since prior 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.