Dirichlet Process Gaussian Mixture Models: Choice of the Base Distribution
Dirichlet Process Gaussian Mixture Models: Choice of the Base Distribution
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DOI：
10.1007/s11390-010-9355-8
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发表时间：
2010-07-01
影响因子：
1.9
通讯作者：
Rasmussen, Carl Edward
中科院分区：
文献类型：
--
作者：
Goeruer, Dilan;Rasmussen, Carl Edward
在贝叶斯混合建模框架中，可以推断出对数据进行建模所需的分量数量，因此没有必要明确限制分量的数量。非参数混合模型通过假设无穷多个组分来回避寻找“正确”混合组分数量的问题。本文将Dirichlet过程混合模型转化为无限混合模型，并利用马尔可夫链蒙特卡罗方法进行推理。模型参数的先验规范通常由数学和实际方便性指导。本文的主要目的是比较共轭和非共轭基分布的选择上的一个特殊的类的非线性模型，这是广泛使用的应用程序，狄利克雷过程高斯混合模型（DPGMM）。我们比较计算效率和建模性能的DPGMM定义使用共轭和条件共轭基分布。我们表明，更好的密度模型可以导致使用更广泛的类的先验没有或只有适度增加计算工作量。
In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of components. Nonparametric mixture models sidestep the problem of finding the "correct" number of mixture components by assuming infinitely many components. In this paper Dirichlet process mixture (DPM) models are cast as infinite mixture models and inference using Markov chain Monte Carlo is described. The specification of the priors on the model parameters is often guided by mathematical and practical convenience. The primary goal of this paper is to compare the choice of conjugate and non-conjugate base distributions on a particular class of DPM models which is widely used in applications, the Dirichlet process Gaussian mixture model (DPGMM). We compare computational efficiency and modeling performance of DPGMM defined using a conjugate and a conditionally conjugate base distribution. We show that better density models can result from using a wider class of priors with no or only a modest increase in computational effort.