Complete-data likelihood
Definition taught in Mixtures and the EM algorithm, part of Statistical learning
Complete-data likelihood
| Type | Definition |
| Taught in | Mixtures and the EM algorithm |
| Part | Statistical learning |
The complete likelihood and its logarithm are
\begin{align*} L_C(\Psi;X_{\mathrm{all}},Z) &=\prod_{i=1}^{n}\prod_{h=1}^{H}\bigl(\pi_h f_h(\mathbf{x}_i)\bigr)^{z_{ih}},\\ \ell_C(\Psi;X_{\mathrm{all}},Z) &=\sum_{i=1}^{n}\sum_{h=1}^{H}z_{ih}\bigl[\ln\pi_h+\ln f_h(\mathbf{x}_i;\theta_h)\bigr]. \end{align*}
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 · Monotonicity of EM · Likelihood function · Missing data · Finite mixture model · Posterior membership · Likelihood of a normal mixture