Gaussian Mixture Model EM Algorithm

This article explores the Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM). This algorithm enables computational estimation of three critical parameters: mixture weights, mean vectors, and covariance matrices for each Gaussian component. The iterative process involves two key phases: E-step computes posterior probabilities using current parameters, while M-step updates parameters based on expected sufficient statistics. GMMs provide superior approximation capabilities for complex distributions compared to single Gaussians, making them valuable for analyzing diverse phenomena with multimodal characteristics. Although alternative algorithms exist for mixture models, the GMM EM algorithm remains particularly useful for understanding distribution properties through its probabilistic framework and convergence guarantees. Practical implementation typically requires initialization strategies, convergence criteria checks, and regularization techniques for covariance matrices to ensure numerical stability.