Model Selection for Mixture Models – Perspectives and Strategies
Model Selection for Mixture Models – Perspectives and Strategies
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DOI：
10.1201/9780429055911-7
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
G. Celeux;Sylvia Fruewirth-Schnatter;C. Robert
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文献类型：
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作者：
G. Celeux;Sylvia Fruewirth-Schnatter;C. Robert
确定有限混合分布中分量G的个数是一个重要而困难的推理问题。这是一个非常重要的问题，因为关于所得模型的统计推断对G的值高度敏感。选择错误的G值可能会产生较差的密度估计。从理论的角度来看，这也是一个最困难的问题，因为它涉及到混合模型的不可识别性问题。从实际的角度来看，这是一个最相关的问题，因为组分G的数量的含义与混合分布的建模目的密切相关。在本章中，我们区分了在第2节中选择G作为密度估计问题和在第3节中选择基于模型的聚类框架中的G。这两个部分都讨论了频率论和贝叶斯方法。在总结这个问题的病态性质之前，我们在这里提出一些贝叶斯解决方案，以解决在混合物中选择“正确”成分数量的不同解释。
Determining the number G of components in a finite mixture distribution is an important and difficult inference issue. This is a most important question, because statistical inference about the resulting model is highly sensitive to the value of G. Selecting an erroneous value of G may produce a poor density estimate. This is also a most difficult question from a theoretical perspective as it relates to unidentifiability issues of the mixture model. This is further a most relevant question from a practical viewpoint since the meaning of the number of components G is strongly related to the modelling purpose of a mixture distribution. We distinguish in this chapter between selecting G as a density estimation problem in Section 2 and selecting G in a model-based clustering framework in Section 3. Both sections discuss frequentist as well as Bayesian approaches. We present here some of the Bayesian solutions to the different interpretations of picking the "right" number of components in a mixture, before concluding on the ill-posed nature of the question.