Finite mixture model
Definition taught in Mixtures and the EM algorithm, part of Statistical learning
Finite mixture model
| Type | Definition |
| Taught in | Mixtures and the EM algorithm |
| Part | Statistical learning |
| Questions using it | 10 |
A finite mixture model gives the data a density that is a finite weighted sum of component densities,
f(x)=\sum_{h=1}^{H}\pi_h f_h(x), \qquad 0\le\pi_h\le 1, \qquad \sum_{h=1}^{H}\pi_h=1.
Here H is the number of components, \pi_h is the probability that an observation is drawn from component h, and f_h is the density of that component. Equivalently, each observation comes from one of a finite collection of parametric distributions.
Used in
- Taught in Mixtures and the EM algorithm, where the derivation and examples are.
- Also used in Bayesian foundations · Model selection for stochastic models · Hierarchical clustering and kernel density estimation · Statistical classifiers and discriminant analysis · Classification trees · Networks in practice
- Questions that use it (10) — The within-cluster sum cannot choose K (answer) · Euclidean clusters and mixture components · Mean and variance of a mixture · An E step · An M step (answer) · Mixtures versus K-means · A tempting wrong turn · Choosing model complexity (answer) · Mixture selection and uncertainty · A tempting wrong turn (answer)
- All 7 questions on Mixtures and the EM algorithm
See also
Identifiability · Label switching · Missing data · Monotonicity of EM · Posterior membership · Complete-data likelihood · EM for a normal mixture · Likelihood of a normal mixture