MATLAB Implementation of the EM Algorithm with Code Explanations

I would like to share a MATLAB implementation of the EM algorithm to help developers gain deeper insights into its practical execution process.

First, let's revisit the conceptual foundation of the EM algorithm. The Expectation-Maximization algorithm is an iterative method for estimating parameters in probabilistic models containing latent variables. Its core mechanism involves alternating between an Expectation step (E-step) that computes posterior probabilities of latent variables given current parameters, and a Maximization step (M-step) that updates parameters by maximizing the expected complete-data log-likelihood. The algorithm iteratively refines parameter estimates until convergence criteria are met.

Now, examining this MATLAB implementation reveals a straightforward structure ideal for educational purposes. The code typically initializes with random parameter guesses, then enters a loop containing: 1) E-step implementation using probability density functions (e.g., normpdf for Gaussian mixtures) to compute responsibilities, and 2) M-step involving weighted parameter updates through matrix operations. For enhanced clarity, we could introduce descriptive variable names like 'log_likelihood_trace' to track convergence, add inline comments explaining key MATLAB functions such as array broadcasting in probability calculations, and implement convergence checks using relative tolerance thresholds. The code might also benefit from visualization components showing parameter evolution during iterations.

In summary, this implementation provides a practical framework for understanding the EM algorithm's mechanics. Developers can further optimize performance by vectorizing loops, implementing early stopping criteria, or adding regularization to prevent overfitting. I hope this resource facilitates productive learning and encourages collaborative improvements to the codebase.