Acceleration Of The EM Algorithm Using The Vector Iteration Of ?~2 Process And The Vector ? Algorithm

Expectation maximization(EM)algorithm is a method to obtain maximum like-lihood estimation in the problem of missing data.Because of its simplicity,flexibil-ity and stability(the likelihood increases monotonously),the EM algorithm has been widely concerned,studied and applied by industry and academia.However,in many applications,the EM algorithm converges very slowly.Therefore,many scholars have proposed various methods for accelerating the convergence speed of the EM algorithm.Inspired by previous research——the application of the vector ?2 process to accelerate the EM algorithm,this paper considers two convergence acceleration methods,namely the vector iteration of ?2 process and the vector ? algorithm.We provide proofs and experiments to confirm that the acceleration effect of these methods is better than that of the vector ?2 process,The new sequence generated when the vector ? algorithm is used to accelerate the EM algorithm can steadily converge to the limit.However,in some statistical models,the sequence obtained by the iteration of ?2 process converges faster.These methods considered in this paper not only inherit the advantages of the EM algorithm,but they also perform better when the convergence conditions are stricter.For the program of these two algorithms,the user only needs to make minor and neces-sary modifications(eg:EM algorithm iteration formula and parameter initialization),and without special algorithm design for different models.They can accelerate all statistical models using EM algorithm,with versatility and easy operation.This article provides four model examples to show their effectiveness,written in Rstudio,and linked to the code of all experiments:https://github.com/XinlingQiu/EM-epsilon-.