Expectation-Maximization Algorithm

02 Nov 2024

🚧 Work in progress…

This article will cover the Expectation-Maximization (EM) algorithm, a powerful iterative method for finding maximum likelihood estimates in models with latent variables.

Topics to cover:

• Introduction to latent variable models
• The challenge of maximum likelihood with hidden variables
• The EM algorithm framework
• E-step: Computing expected values of latent variables
• M-step: Maximizing the expected log-likelihood
• Convergence properties and guarantees
• Mathematical derivation using Jensen’s inequality
• Classic applications:
  • Gaussian Mixture Models (GMM)
  • Hidden Markov Models (HMM)
  • Factor Analysis
• Variants: Hard EM, Incremental EM, Online EM
• Relationship to K-means clustering
• When EM works well and its limitations
• Practical implementation tips