Variational Bayesian Learning Of Mixed Erlang Model

In this paper,we focus on the application of Bayesian variational methods for mixed Erlang Model.Mixed Erlang Model forms a versatile,yet analytically tractable,class of distributions making them suitable for multivariate density estimation.In addition,the distribution in the weak convergence of the continuous distribution of the space is dense.The above good properties make the multicomponent Erlang model suitable for multivariate density estimation.On this basis,we propose a flexible and effective fitting process for mixed Erlang model,called CMM-VBEM algorithm.The algorithm is divided into two parts.The first part is the selection of initial value.Using the K-Means clustering method to estimate the initial value of the parameter,it is proved that the method greatly improves the validity of the initial value selection.In addition,the Bayesian Information Criterion(BIC)is used to select the number of mixing.The second is the VBEM algorithm.The process is based on the Bayesian variational method and the iterative use of the EM algorithm to introduce the effective estimation and adjustment strategy for the parameters such as shape parameters and mixed weights.Compared with the traditional EM algorithm and other mixed models commonly used methods,our method has several advantages.First,it can prevent over-fitting problems,especially when the amount of data is less time,our method is more obvious advantages;In addition,the CMM-VBEM algorithm succeeds in avoiding local optimal problems.In this paper,the proposed CMM-VBEM algorithm is validated by simulating the data and the actual data.A variety of test methods(including Kolmogorov-Smirnov test,Anderson-Darling test and Cramer-von Mises test)were validated by graphic verification(including empirical histogram,QQ plot,PP plot,contour map),and verified from various aspects,Full description of our algorithm in the data fitting effect is good.The effectiveness of the proposed algorithm is demonstrated on simulated as well as real data sets.These all proved that our algorithm perform well in data fitting.