EM算法研究与应用

Research and Application of EM Algorithm

引入了可处理缺失数据的EM算法。EM算法是一种迭代算法,每一次迭代都能保证似然函数值增加,并且收敛到一个局部极大值。对EM算法的基本原理和实施步骤进行了分析。算法的命名,是因为算法的每一迭代包括两步:第一步求期望(Expectation Step),称为E步;第二步求极大值(Maximization Step),称为M步。EM算法主要用来计算基于不完全数据的极大似然估计。在此基础上,把EM算法融合到状态空间模型的参数估计问题。给出了基于Kalman平滑和算法的线性状态空间模型参数估计方法。

Following the description of traditional maximum likelihood estimation methods and the discussions on their disadvantages. EM algorithm is an iterative algorithm, every iteration to ensure that the likelihood ftmetion can be increased, and the convergence to a local maxima. Presents an EM algorithm that can be used to deal with missing data problems, where the details of the EM algorithm and its realization procedure have been analyzed. Algorithm named because each iterative algorithm includes two steps： the first step in seeking expectations （Expectation Step）, known as the E step; the second step for maxima （Maximization Step）, known as step- by- step M. EM algorithm used to ealeulate the prineipal based on incomplete data, maximum likelihood estimation. This is then followed by applying the proposed EM algorithm to the parameter estimation of state space models. The paper also presents the Kalman smoothing based parameter estimation methods for linear state spaee models.