Nonparametric empirical Bayes for the Dirichlet process mixture model
Nonparametric empirical Bayes for the Dirichlet process mixture model
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DOI：
10.1007/s11222-006-5196-2
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发表时间：
2006-03-01
影响因子：
2.2
通讯作者：
Jordan, MI
中科院分区：
文献类型：
--
作者：
McAuliffe, JD;Blei, DM;Jordan, MI
Dirichlet过程先验允许灵活的非参数混合建模。混合组分的数量没有预先指定，并且可以随着新数据的到来而增加。然而，基于狄利克雷过程先验的分析对参数的选择敏感，包括无限维分布参数G（0）。大多数以前的应用程序要么固定G（0）作为一个参数族的成员，或处理G（0）在贝叶斯的方式，使用参数先验规范。相反，我们已经开发了一种自适应非参数方法来构造G（0）的光滑估计。我们结合联合收割机这种方法与技术估计阿尔法，其他狄利克雷过程参数，这是由现有的表征其最大似然估计的启发。总之，这些估计程序产生一个灵活的经验贝叶斯处理狄利克雷过程的混合物。这样的处理是有用的情况下，G（0）的光滑点估计是内在的利益，或G（0）的结构不能方便地与通常的参数先验族建模。模拟和真实世界的数据集的分析说明了这种方法的鲁棒性。
The Dirichlet process prior allows flexible nonparametric mixture modeling. The number of mixture components is not specified in advance and can grow as new data arrive. However, analyses based on the Dirichlet process prior are sensitive to the choice of the parameters, including an infinite-dimensional distributional parameter G(0). Most previous applications have either fixed G(0) as a member of a parametric family or treated G(0) in a Bayesian fashion, using parametric prior specifications. In contrast, we have developed an adaptive nonparametric method for constructing smooth estimates of G(0). We combine this method with a technique for estimating alpha, the other Dirichlet process parameter, that is inspired by an existing characterization of its maximum-likelihood estimator. Together, these estimation procedures yield a flexible empirical Bayes treatment of Dirichlet process mixtures. Such a treatment is useful in situations where smooth point estimates of G(0) are of intrinsic interest, or where the structure of G(0) cannot be conveniently modeled with the usual parametric prior families. Analysis of simulated and real-world datasets illustrates the robustness of this approach.