EM算法的BFGS加速算法

A BFGS Acceleration Method of the EM Algorithm

EM算法是一种求参数极大似然估计的迭代算法,在处理不完全数据中有重要应用。EM算法实现简单,数值计算稳定,存储量小,具有良好的全局收敛性,但EM算法收敛速度慢只是次线性的收敛速度,妨碍了EM算法的应用。现已提出了多种加速EM算法收敛的方法。本文是在EM算法的拟Newton加速算法的基础上,使用非线性规划中对称秩2校正公式(BFGS公式)给出了一种新的加速EM算法收敛的方法。它是针对EM的M步的,在共享EM算法单调增加似然函数值和稳定收敛的基础上提高EM算法的收敛速度。最后用数值试验结果验证了该加速算法的有效性和可行性。

EM Algorithm is a maximum likelihood parameter estimation itemtive algorithm. It is simple and stable to implement and ensuring iterative convergence , but it has slowly convergence. In this paper on the basis of Quasi-Newton acceleration method, the authors have used nonlinear programming modified formula and showed a new method for accelerating the EM algorithm. Moreover a comparison of EM algorithm and modified method was made. The new method has much faster convergence than the EM algorithm.