# Statistical Mixture Model

A Statistical Mixture Model is a probabilistic generative model that can express a mixture probability function (with mixture model components).

## References

### 2013

• (Wikipedia, 2011) ⇒ http://en.wikipedia.org/wiki/Mixture_model
• QUOTE:In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data-set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population. However, while problems associated with "mixture distributions" relate to deriving the properties of the overall population from those of the sub-populations, "mixture models" are used to make statistical inferences about the properties of the sub-populations given only observations on the pooled population, without sub-population-identity information.

Some ways of implementing mixture models involve steps that attribute postulated sub-population-identities to individual observations (or weights towards such sub-populations), in which case these can be regarded as types of unsupervised learning or clustering procedures. However not all inference procedures involve such steps.

Mixture models should not be confused with models for compositional data, i.e., data whose components are constrained to sum to a constant value (1, 100%, etc.).

### 1993

• (Utans, 1993) ⇒ J. Utans. (1993). “Mixture Models and EM Algorithms for Object Recognition within Compositional Hierarchies.” ICSI Berkeley Technical Report TR-93-004.