Mixture models with a prior on the number of components.
Mixture models with a prior on the number of components.
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DOI：
10.1080/01621459.2016.1255636
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发表时间：
2018
影响因子：
3.7
通讯作者：
Harrison MT
中科院分区：
文献类型：
--
作者：
Miller JW;Harrison MT
一个自然的贝叶斯方法的混合模型与未知数量的组件是采取通常的有限混合模型与对称Dirichlet权重，并把一个先验的组件的数量，也就是说，使用混合有限的混合物（MFM）。最常用的推理方法是可逆跳跃马尔可夫链蒙特卡罗，但它可以设计好的可逆跳跃移动，特别是在高维空间。与此同时，Dirichlet过程混合物（Dirichlet process mixture，简写为DIBM）模型的采样器相对简单，易于适应新的应用。事实证明，事实上，DPM的许多基本属性也表现出MFM-可交换分区分布，餐厅过程，随机测量表示和棒断裂表示-至关重要的是，MFM类似物足够简单，它们可以像相应的DPMs属性一样使用。因此，许多在DPM中为推理开发的强大方法也可以直接应用于MFM;这简化了MFM的实现，并可以大大改善混合。我们用真实的和模拟的数据来说明，包括用于区分癌症亚型的高维基因表达数据。
A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric Dirichlet weights, and put a prior on the number of components—that is, to use a mixture of finite mixtures (MFM). The most commonly-used method of inference for MFMs is reversible jump Markov chain Monte Carlo, but it can be nontrivial to design good reversible jump moves, especially in high-dimensional spaces. Meanwhile, there are samplers for Dirichlet process mixture (DPM) models that are relatively simple and are easily adapted to new applications. It turns out that, in fact, many of the essential properties of DPMs are also exhibited by MFMs—an exchangeable partition distribution, restaurant process, random measure representation, and stick-breaking representation—and crucially, the MFM analogues are simple enough that they can be used much like the corresponding DPM properties. Consequently, many of the powerful methods developed for inference in DPMs can be directly applied to MFMs as well; this simplifies the implementation of MFMs and can substantially improve mixing. We illustrate with real and simulated data, including high-dimensional gene expression data used to discriminate cancer subtypes.
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