有限贝塔刘维尔混合模型的变分学习及其应用

Variational Learning for Finite Beta-Liouville Mixture Models and Its Application

由于贝塔刘维尔分布的共轭先验分布中存在积分表达式,贝叶斯估计有限贝塔刘维尔混合模型参数异常困难.本文提出利用变分贝叶斯学习模型参数,采用gamma分布作为近似的先验分布并使用合理的非线性近似技术,得到了后验分布的近似解.与常用的EM算法相比,该方法能够同时估计模型参数和确定分量数,且避免了过拟合的问题.在合成数据集及场景分类问题上进行了大量的实验,实验结果验证了本文所提方法的有效性.

Since the integration expression is present in the conjugate prior distribution,Bayesian estimation of the parameters in finite Beta-Liouville mixture models（BLM）is analytically inlractable. In this paper, an approach based on the variational inference framework is proposed. Adopting gamma distributions to approximate the prior distributions of the parameter in BI.aM and using some reasonable non-linear approximations; the closed form solution for the posterior distribution of the parameters is obtained. Compared to the conventional expectation maximization （EM）algorithm, the proposed algorithm is able to simultaneously estimate the model parameters and determine the number of components; our method also avoids the problem of overfitting. Extensive experi- mental results based on the synthetic data sets and scenes classification show that the proposed method is efficient and feasible in terms of parameter estimation and model selection.