Posterior membership
Definition taught in Mixtures and the EM algorithm, part of Statistical learning
Posterior membership
| Type | Definition |
| Taught in | Mixtures and the EM algorithm |
| Part | Statistical learning |
| Questions using it | 4 |
The posterior probability that observation \mathbf{x} came from component h, evaluated at \Psi, is
\tau_h(\mathbf{x};\Psi) =\frac{\pi_h f_h(\mathbf{x};\theta_h)}{\sum_{m=1}^{H}\pi_m f_m(\mathbf{x};\theta_m)},
where \theta_h holds the mean and covariance of component h. These probabilities are the responsibilities. They are nonnegative and sum to one over h.
Used in
- Taught in Mixtures and the EM algorithm, where the derivation and examples are.
- Questions that use it (4) — Euclidean clusters and mixture components (answer) · An E step (answer) · An M step · Mixtures versus K-means (answer)
- All 7 questions on Mixtures and the EM algorithm
See also
Bayes’ rule · Posterior class probability · Bayes classifier · Mean vector and covariance matrix · Finite mixture model · Complete-data likelihood · EM for a normal mixture · Monotonicity of EM