EM Algorithm: A Fundamental Approach in Machine Learning

In the field of machine learning, the EM (Expectation-Maximization) algorithm serves as a fundamental method for estimating parameters in probabilistic models containing latent variables. The core concept involves iteratively estimating model parameters when they are not fully observable. Each iteration consists of two distinct phases: the E-step and M-step. During the E-step, the algorithm computes the posterior probability distribution of latent variables using current parameter estimates - typically implemented through probability calculations using Gaussian density functions in mixture models. The M-step then maximizes the likelihood function to derive updated parameters, often involving mean and covariance recalculations for each mixture component. This implementation provides the simplest practical demonstration of EM algorithm applied to Gaussian Mixture Models, featuring clear separation of E-step and M-step functions with commented code to help understand both the theoretical foundation and practical implementation details. The code structure includes initialization routines, convergence checks, and visualization components to monitor algorithm progress.