Gibbs Sampling for (Coupled) Infinite Mixture Models in the Stick Breaking Representation
Gibbs Sampling for (Coupled) Infinite Mixture Models in the Stick Breaking Representation
复制标题
断棍表示中（耦合）无限混合模型的吉布斯采样
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
M. Welling
中科院分区：
文献类型：
--
作者：
I. Porteous;A. Ihler;Padhraic Smyth;M. Welling
非参数贝叶斯方法聚类，信息检索，语言建模和对象识别最近显示出巨大的希望，作为一个新的范例无监督数据分析。大多数的贡献都集中在狄利克雷过程的混合物模型或扩展，有效的吉布斯采样器存在。在本文中，我们探讨吉布斯采样无限复杂的混合模型在棒断裂表示。这种表示的优点是提高了建模的灵活性。例如，可以设计簇大小的先验分布，或者在参数水平上耦合多个无限混合模型（例如，随时间）（即依赖狄利克雷过程模型）。然而，无限混合模型的吉布斯采样器（最近在统计文献中介绍）似乎在集群标签上混合得很差。除其他问题外，这可能会产生不利影响，即耦合混合模型中相同聚类的标签会混淆。我们在这些采样器中引入了额外的移动，以改善集群标签的混合，并使集群保持一致。风暴轨迹建模的应用程序来说明这些想法。
Nonparametric Bayesian approaches to clustering, information retrieval, language modeling and object recognition have recently shown great promise as a new paradigm for unsupervised data analysis. Most contributions have focused on the Dirichlet process mixture models or extensions thereof for which efficient Gibbs samplers exist. In this paper we explore Gibbs samplers for infinite complexity mixture models in the stick breaking representation. The advantage of this representation is improved modeling flexibility. For instance, one can design the prior distribution over cluster sizes or couple multiple infinite mixture models (e.g. over time) at the level of their parameters (i.e. the dependent Dirichlet process model). However, Gibbs samplers for infinite mixture models (as recently introduced in the statistics literature) seem to mix poorly over cluster labels. Among others issues, this can have the adverse effect that labels for the same cluster in coupled mixture models are mixed up. We introduce additional moves in these samplers to improve mixing over cluster labels and to bring clusters into correspondence. An application to modeling of storm trajectories is used to illustrate these ideas.