Application Of EM Algorithm And Its Improved Algorithm To Parameter Estimation

Expectation maximization algorithm,called EM algorithm,is a very important iterative algorithm in machine learning,and is mainly used to solve parameter estimation problem on the condition of missing data.Besides,EM algorithm which transforms the incomplete data to complete data by introducing the potential data is a kind of data add algorithm.Further,EM algorithm analyze the complete data likelihood function to achieve a deeper level of statistical analysis.At the same time,the EM algorithm is simple,stable and so on,and this performances make the algorithm more popular in in dealing situation with data loss.Of course,there are many defects in EM algorithm,such as slow convergence and it is difficult to give a clear expression of the E step or M step in some cases.It is these defects that cause a lot of inconvenience to statistical analysis.Many scholars have proposed a variety of improved EM algorithm and a hybrid algorithm which combines EM algorithm with other algorithms.Combining the existing research results,this paper focuses on the application of EM algorithm and its improved algorithm in parameter estimation of exponential family mixed distribution and multi-layer linear model.The main tasks and achievements of this paper are as follows:(1)The research background and the domestic and foreign research literature of EM algorithm and its improved algorithm are reviewed,and the application status of EM algorithm and its improved algorithm in solving the problem of missing data parameter estimation is understood.(2)The basic principles of EM algorithm,MCEM algorithm,MCEM acceleration algorithm and improved MCEM acceleration algorithm are studied.The iterative steps,advantages and disadvantages of each algorithm are given.For the four algorithms,this paper gives an example analysis,and the results of parameter iteration are accurate,and the iterative speed of parameter iteration is compared.(3)According to the exponential mixture distribution,the derivation process of parameter estimation of EM algorithm is given for general exponential family mixed distribution,and the iterative formula is given for common exponential family mixed distribution under EM algorithm and MCEM algorithm.Accurate estimated value are obtained through simulation.The research fills the gap of parameter estimation of exponential mixture distribution based on EM algorithm and MCEM algorithm.(4)For the multi-layer linear model,the iterative step of parameter estimation of the EM model and the MCEM algorithm is given,and the numerical simulation is carried out based on the iterative step.The simulation results show that the parameter estimation is accurate.The problem of parameter estimation of multi-layer linear model based on EM and MCEM algorithm is studied,and it overcame the shortcomings of the maximum likelihood estimation method for estimating the parameters of multi-layer linear model.