[Probability] EM Algorithm

EM Algorithm

  • For incomplete data case of Maximum Likelihood
  • Auxiliary function
    • No learning rate
    • Monotonic convergence (each iteration improves L)
  • Comparison with other numerical methods
    • Gradient Descent: Asymptotic but not monotonic convergence
    • Newton’s Method: Monotonic convergence, but highly unstable

Problem

Insight

We can find an auxiliary function that guarantees monotonic convergence

Derivation

Algorithm

  1. Initialize CPT to any value (non-zero)
  2. Repeat following until convergence

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