Random Partition Distribution Indexed by Pairwise Information.
Random Partition Distribution Indexed by Pairwise Information.
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DOI：
10.1080/01621459.2016.1165103
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发表时间：
2017
影响因子：
3.7
通讯作者：
Tsai JW
中科院分区：
文献类型：
--
作者：
Dahl DB;Day R;Tsai JW
我们提出了一种由两两相似度信息索引的随机分区分布，使得与相似度相容的分区被赋予更大的概率。以距离的形式使用成对相似性在一些聚类算法（例如，分层聚类）中很常见，但是我们展示了如何使用这种类型的信息来定义灵活贝叶斯建模的先验分区分布。该分布的一个定义特征是，它在给定数量的子集内的分区之间分配概率，但它不会在具有不同数量子集的分区集之间转移概率。我们的分布将更多的概率放在分组相似项的分区上，但保持具有给定数量子集的分区的总概率不变。子集数量的分布（及其矩）是封闭形式的，不是相似度的函数。我们的公式具有明确的概率质量函数（具有可处理的归一化常数），因此完整的MCMC方法套件可用于后验推理。我们将我们的分布与几个现有的分区分布进行比较，表明我们的公式具有吸引人的性质。我们提供了三个演示，以突出我们的发行版的特性和相对性能。
We propose a random partition distribution indexed by pairwise similarity information such that partitions compatible with the similarities are given more probability. The use of pairwise similarities, in the form of distances, is common in some clustering algorithms (e.g., hierarchical clustering), but we show how to use this type of information to define a prior partition distribution for flexible Bayesian modeling. A defining feature of the distribution is that it allocates probability among partitions within a given number of subsets, but it does not shift probability among sets of partitions with different numbers of subsets. Our distribution places more probability on partitions that group similar items yet keeps the total probability of partitions with a given number of subsets constant. The distribution of the number of subsets (and its moments) is available in closed-form and is not a function of the similarities. Our formulation has an explicit probability mass function (with a tractable normalizing constant) so the full suite of MCMC methods may be used for posterior inference. We compare our distribution with several existing partition distributions, showing that our formulation has attractive properties. We provide three demonstrations to highlight the features and relative performance of our distribution.