Monotonicity of EM
Theorem taught in Mixtures and the EM algorithm, part of Statistical learning
Monotonicity of EM
| Type | Theorem |
| Taught in | Mixtures and the EM algorithm |
| Part | Statistical learning |
An exact EM step cannot decrease the observed log-likelihood (Dempster, Laird, and Rubin, 1977). Convergence of the likelihood values requires an upper bound. Convergence of the parameters requires further conditions. Under the regularity conditions studied by Wu (1983), limit points are stationary. A stationary point of a mixture likelihood can fail to be a global maximum.
Used in
- Taught in Mixtures and the EM algorithm, where the derivation and examples are.
- All 7 questions on Mixtures and the EM algorithm
See also
EM algorithm · EM for a normal mixture · Complete-data likelihood · Likelihood function · Finite mixture model · Posterior membership · Likelihood of a normal mixture · What the stationary equations suggest