Hierarchical Dirichlet processes
Hierarchical Dirichlet processes
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DOI：
10.1198/016214506000000302
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发表时间：
2006-12-01
影响因子：
3.7
通讯作者：
Blei, David M.
中科院分区：
文献类型：
--
作者：
Teh, Yee Whye;Jordan, Michael I.;Blei, David M.
我们考虑涉及数据组的问题，其中组内的每个观测值都来自一个混合模型，并且希望在组之间共享混合成分。我们假设混合成分的数量是先验未知的，并且要从数据中推断出来。在这种情况下，自然要考虑狄利克雷过程集，每组一个，其中狄利克雷过程众所周知的聚类性质为每组内混合成分的数量提供了一个非参数先验。鉴于我们希望将不同组中的混合模型联系起来，我们考虑一个层次模型，特别是其中子狄利克雷过程的基测度本身根据一个狄利克雷过程分布的模型。这样一个基测度是离散的，子狄利克雷过程必然共享原子。因此，正如所期望的，不同组中的混合模型必然共享混合成分。我们根据断棍过程以及我们称为“中餐馆连锁”的中国餐馆过程的一种推广来讨论层次狄利克雷过程的表示。我们提出用于层次狄利克雷过程混合中的后验推断的马尔可夫链蒙特卡罗算法，并描述在信息检索和文本建模问题中的应用。
We consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from the data. In this setting it is natural to consider sets of Dirichlet processes, one for each group, where the well-known clustering property of the Dirichlet process provides a nonparametric prior for the number of mixture components within each group. Given our desire to tie the mixture models in the various groups, we consider a hierarchical model, specifically one in which the base measure for the child Dirichlet processes is itself distributed according to a Dirichlet process. Such a base measure being discrete, the child Dirichlet processes necessarily share atoms. Thus, as desired, the mixture models in the different groups necessarily share mixture components. We discuss representations of hierarchical Dirichlet processes in terms of a stick-breaking process, and a generalization of the Chinese restaurant process that we refer to as the "Chinese restaurant franchise." We present Markov chain Monte Carlo algorithms for posterior inference in hierarchical Dirichlet process mixtures and describe applications to problems in information retrieval and text modeling.