论文标题
为什么有钱人变得更富有？关于随机分区模型的平衡
Why the Rich Get Richer? On the Balancedness of Random Partition Models
论文作者
论文摘要
随机分区模型被广泛用于贝叶斯方法中，用于各种聚类任务，例如混合模型，主题模型和社区检测问题。尽管已经对随机分区模型诱导的簇数量进行了广泛的研究，但在很大程度上忽略了有关分区平衡性的另一个重要模型属性。我们通过分析模型如何将概率分配给具有不同级别的平衡度的分区，从而制定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，许多现有流行的随机分区模型的“丰富”特征是两个共同假设的必然结果：产品形式的交换性和投影率。我们提出了一种比较随机分区模型的平衡性的原则方法，该模型可以更好地了解哪些模型更好，而对于不同的应用程序而言，哪些模型的工作方式更好。我们还介绍了“富裕者”随机分区模型，并说明了它们在实体解决任务中的应用。
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.
