Parameter Estimation Using the EM Algorithm

The EM (Expectation-Maximization) algorithm primarily serves for parameter estimation in Gaussian Mixture Models. This iterative optimization algorithm estimates GMM parameters given observed data and initial parameter values. Gaussian Mixture Models are statistical models describing complex data distributions comprising multiple Gaussian distributions. The EM algorithm alternates between E-steps and M-steps for parameter estimation: the E-step computes expectations of latent variables using current parameters, while the M-step updates model parameters by maximizing the expected complete-data log-likelihood. Through multiple iterations, the EM algorithm progressively enhances parameter estimation accuracy. Implementation typically involves calculating posterior probabilities in the E-step (using Bayes' theorem) and solving weighted maximum likelihood estimates in the M-step. Key functions may include log-likelihood computation, covariance regularization, and convergence checking. Consequently, the EM algorithm finds widespread application in parameter estimation for Gaussian Mixture Models across various domains including pattern recognition and data clustering.