贝叶斯聚类中控制“富-更富”先验假设重要性的Powered Dirichlet过程
Powered Dirichlet Process for Controlling the Importance of "Rich-Get-Richer" Prior Assumptions in Bayesian Clustering
摘要：
贝叶斯聚类中最常用的先验之一是Dirichlet先验。它可以被描述为一个中国餐馆的过程。这个过程允许在划分数据集时对聚类数进行非参数估计。它的关键特征是“富-更富”属性，该属性假设集群具有线性依赖于人口的先验概率。在本文中，我们表明，这种先验并不总是最好的选择模型数据。我们从狄利克雷-多项分布的修改版本中推导出动力中餐厅过程来回答这个问题。然后，我们开发它的一些基本属性（预期的集群数量，收敛性）。与这方面的最新努力不同，这一新的提法允许直接控制“富-更富”优先的重要性。
英文摘要：
One of the most used priors in Bayesian clustering is the Dirichlet prior. It can be expressed as a Chinese Restaurant Process. This process allows nonparametric estimation of the number of clusters when partitioning datasets. Its key feature is the "rich-get-richer" property, which assumes a cluster has an a priori probability to get chosen linearly dependent on population. In this paper, we show that such prior is not always the best choice to model data. We derive the Powered Chinese Restaurant process from a modified version of the Dirichlet-Multinomial distribution to answer this problem. We then develop some of its fundamental properties (expected number of clusters, convergence). Unlike state-of-the-art efforts in this direction, this new formulation allows for direct control of the importance of the "rich-get-richer" prior.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
