基于高斯混合模型案例的EM算法教学设计
Teaching Design of EM Algorithm Based on Gaussian Mixture Model Case

EM (Expectation Maximization)算法是统计学中的核心算法，也是本校近代数理统计课程教学过程中的一个重难点。论文采用案例式、启发式、研讨式教学方法，以基于高斯混合模型(GMM)的轴承退化阶段划分问题为例，引导学生发现隐变量模型极大似然估计(MLE)存在的困难，设计问题链启发学生探寻参数估计的数值方法，并总结出EM算法的一般过程。基于matlab编程可视化EM算法下的GMM模型参数更新过程，对比MLE目标函数和EM迭代目标函数，分析EM算法的内涵思想并结合图形进行直观展示，并且挖掘其中蕴含的思政元素，在知识传授的同时实现价值塑造。
Expectation maximization (EM) algorithm is a core algorithm in statistics and also a key and difficult point in the teaching process of modern mathematical statistics courses in our school. The paper adopts a case-based and heuristic teaching method, taking the Gaussian Mixture Model (GMM) based bearing degradation stage division problem as an example, guiding students to discover the difficulties of maximum likelihood estimation (MLE) in the latent variable model, designing a problem chain to inspire students to explore numerical methods for parameter estimation, and summarizing the general process of EM algorithm. Based on Matlab programming, the parameter update process of GMM based on EM algorithm is visualized. Comparing the MLE objective function and EM iteration objective function, the intrinsic thought of EM algorithm is analyzed and visually displayed with graphics. The ideological and political elements are also explored, so as to achieve value shaping while knowledge transmission.