Markov chain Monte Carlo in approximate Dirichlet and beta two-parameter process hierarchical models
近似狄利克雷与贝塔双参数过程层级模型中的 MCMCAI 解读 ↓
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近似狄利克雷与贝塔双参数过程层级模型中的 MCMC
- 研究问题
- 如何以易构造的随机概率测度近似非参数先验，使层级模型能够高效运行 MCMC，并监测近似是否充分？
- 方法与思路
- 作者构造狄利克雷过程的截断与弱极限近似，并将截断扩展至贝塔双参数过程，结合分块坐标更新拟合后验。
- 材料陈述的贡献
- 摘要称截断充分性可由 Gibbs 输出监测，且狄利克雷过程截断近似在相同计算量下具有更高的近似精度。
- 阅读关注点
- 应核对截断误差及监测量的定义、分块更新的混合表现，并区分近似精度比较与混合成分数匹配的经验陈述。
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- 仅据版本未注明的 OpenAlex 索引摘要；未给出误差度量、截断选择及比较条件，不能据此保证任意模型的采样效率。
原文摘要
We present some easy-to-construct random probability measures which approximate the Dirichlet process and an extension which we will call the beta two-parameter process. The nature of these constructions makes it simple to implement Markov chain Monte Carlo algorithms for fitting nonparametric hierarchical models. For the Dirichlet process, we consider a truncation approximation as well as a weak limit approximation based on a mixture of Dirichlet processes. The same type of truncation approximation can also be applied to the beta two-parameter process. Both methods lead to posteriors which can be fitted using Markov chain Monte Carlo algorithms that take advantage of blocked coordinate updates. These algorithms promote rapid mixing of the Markov chain and can be readily applied to normal mean mixture models and to density estimation problems. We prefer the truncation approximations, since a simple device for monitoring the adequacy of the approximation can be easily computed from the output of the Gibbs sampler. Furthermore, for the Dirichlet process, the truncation approximation offers an exponentially higher degree of accuracy over the weak limit approximation for the same computational effort. We also find that a certain beta two-parameter process may be suitable for finite mixture modelling because the distinct number of sampled values from this process tends to match closely the number of components of the underlying mixture distribution.