Why the Rich Get Richer? On the Balancedness of Random Partition Models
Why the Rich Get Richer? On the Balancedness of Random Partition Models
复制标题
DOI：
--
复制
发表时间：
2022-01
期刊：
影响因子：
--
通讯作者：
Changwoo J. Lee-;H. Sang
中科院分区：
文献类型：
--
作者：
Changwoo J. Lee-;H. Sang
随机划分模型广泛应用于各种聚类任务的贝叶斯方法中，例如混合模型、主题模型和社区检测问题。虽然随机分区模型引起的聚类数量已被广泛研究，但关于分区平衡性的另一个重要模型属性在很大程度上被忽视了。通过分析模型如何将概率分配给具有不同平衡性水平的分区，我们制定了一个框架来定义和理论上研究可交换随机分区模型的平衡性。我们证明，许多现有流行随机分配模型的“富者愈富”特征是两个常见假设的必然结果：产品形式可交换性和投射性。我们提出了一种比较随机分区模型平衡性的原则性方法，这可以更好地理解哪些模型对于不同的应用程序效果更好，哪些模型效果不佳。我们还介绍了“富者变穷”随机划分模型，并说明了它们在实体解析任务中的应用。
Random partition models are widely used in Bayesian methods for various clustering tasks, such as mixture models, topic models, and community detection problems. While the number of clusters induced by random partition models has been studied extensively, another important model property regarding the balancedness of partition has been largely neglected. We formulate a framework to define and theoretically study the balancedness of exchangeable random partition models, by analyzing how a model assigns probabilities to partitions with different levels of balancedness. We demonstrate that the"rich-get-richer"characteristic of many existing popular random partition models is an inevitable consequence of two common assumptions: product-form exchangeability and projectivity. We propose a principled way to compare the balancedness of random partition models, which gives a better understanding of what model works better and what doesn't for different applications. We also introduce the"rich-get-poorer"random partition models and illustrate their application to entity resolution tasks.