MATLAB Implementation of the EM Algorithm for Parameter Estimation

In this article, we discuss how to use the EM algorithm for training parameters in stochastic process models and provide a MATLAB-based implementation. The EM algorithm serves as a fundamental approach for parameter estimation in Hidden Markov Models (HMMs), which are statistical models describing hidden processes with Markov properties. We will detail the working mechanism of the EM algorithm and demonstrate its implementation in MATLAB, including the iterative Expectation (E-step) and Maximization (M-step) procedures. Starting with basic concepts and principles, we will progressively explore MATLAB implementation techniques such as handling probability distributions using built-in functions like `normpdf` for Gaussian models and optimizing parameters with `fmincon`. The implementation will cover key aspects like log-likelihood computation, convergence checks, and handling missing data. Finally, we address potential issues such as local optima and initialization sensitivity, along with solutions like multiple random restarts, and illustrate practical applications of the algorithm for real-world problems such as sequence analysis and pattern recognition.