贝塔混合模型的变分贝叶斯学习及应用

Variational Bayesian Learning for Beta Mixture Model and Its Application

贝塔混合模型(Beta Mixture Model,BMM)是一种重要的非高斯概率模型,常用于有界数据的统计分析.但是由于其表达式复杂,BMM的参数估计比较困难.针对该问题,本文提出一种高效的变分贝叶斯学习方法进行参数估计.该方法采用形式简单的自由分布,通过不断最大化初始变分目标函数的下界,迭代逼近得到真实的贝叶斯后验分布.在合成数据集与实际数据集上进行实验,实验结果证明了所提出算法的有效性和可行性.

Beta mixture model（ BMM） is an important non-Gaussian probability model,which has been widely used in statistical analysis of the bounded data. It is hard to perform parameter estimation for BMM,due to its complex function format. An efficient variational Bayesian learning method has been proposed to deal with this problem. With the variational distribution and by iteratively maximizing the lower bound of the original variational object function,the approximating distribution which is the closest to the true Bayesian posterior distribution is obtained. Both synthetic and real data are experimented to demonstrate the effectiveness and the merits of the proposed approach.