混合逆狄利克雷分布的变分学习及应用

Variational Learning for Finite Inverted Dirichlet Mixture Models and Applications

混合逆狄利克雷分布是正的非高斯数据分析中一个重要的统计模型.但是利用常用的统计方法比如极大近似然估计、矩估计等往往很难得到模型参数估计的显性解析式.本文提出一个变分贝叶斯学习算法,它能够在估计参数的同时自动确定混合分量数.在合成数据集及实测数据集上的实验结果表明利用变分贝叶斯推理来估计混合逆狄利克雷分布是一种非常有效的方法.

Finite inverted Dirichlet mixture models play an important part in positive non-Gaussian data analysis. However, it is always different to obtain the analytical solutions to model parameters by using conventional approaches such as maximization likelihood estimation and moment estimation. In this paper, we have proposed a variational inference framework. Within this frame- work, pm＂mneter estimation and automatic model selection can be carried out simulta-neously. Experimental results on synthetic and real-world data sets demonslrate the effectiveness and the merits of the proposed approach.