使用具有归一化逆高斯权重的有限混合模型的贝叶斯混合建模
Bayesian mixture modeling using a mixture of finite mixtures with normalized inverse Gaussian weights
AI总结：
研究贝叶斯混合模型中成分数量未知的情况，提出基于归一化逆高斯权重的MFM方法，通过引入潜在变量用块吉布斯采样计算后验，经数值实验和实际数据示例验证性能，还考虑了对动态MFM的扩展。
摘要：
在贝叶斯推理中，对于成分数量未知的混合模型，通常采用有限混合模型，该模型对混合权重和成分数量假设先验分布，即混合的有限混合模型（MFM）。作为权重的先验分布，（对称）狄利克雷分布因共轭性和计算简便而被广泛使用，但其浓度参数的选择会影响后验推断。作为狄利克雷权重的稳健替代方法，本文提出一种基于具有归一化逆高斯权重的MFM方法。其动机类似于在非参数贝叶斯统计中使用归一化逆高斯过程代替狄利克雷过程。通过引入潜在变量，使用块吉布斯采样进行后验计算，无需使用可逆跳跃算法。在阐明与伸缩采样的关系后，还考虑了对动态MFM的扩展。通过数值实验和实际数据示例说明了该方法的性能，包括聚类、密度估计和社区检测。本文的补充材料可在线获取。
英文摘要：
In Bayesian inference for mixture models with an unknown number of components, a finite mixture model is usually employed that assumes prior distributions for mixing weights and the number of components. This model is called a mixture of finite mixtures (MFM). As a prior distribution for the weights, a (symmetric) Dirichlet distribution is widely used for conjugacy and computational simplicity, while the selection of the concentration parameter influences posterior inference. As a robust alternative to Dirichlet weights, we present a method based on a MFM with normalized inverse Gaussian weights. The motivation is similar to the use of normalized inverse Gaussian processes instead of Dirichlet processes in nonparametric Bayesian statistics. Introducing latent variables, the posterior computation is carried out using blocked Gibbs sampling without using the reversible jump algorithm. We also consider extensions to dynamic MFMs after clarifying the relationship with telescoping sampling. The performance of the proposed method is illustrated through some numerical experiments and real data examples, including clustering, density estimation, and community detection. Supplementary materials for this article are available online.
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