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.).
Read more about Mixture Model: Identifiability, Parameter Estimation and System Identification, Extensions, History
Famous quotes containing the words mixture and/or model:
“Nature’s law says that the strong must prevent the weak from living, but only in a newspaper article or textbook can this be packaged into a comprehensible thought. In the soup of everyday life, in the mixture of minutia from which human relations are woven, it is not a law. It is a logical incongruity when both strong and weak fall victim to their mutual relations, unconsciously subservient to some unknown guiding power that stands outside of life, irrelevant to man.”
—Anton Pavlovich Chekhov (1860–1904)
“AIDS occupies such a large part in our awareness because of what it has been taken to represent. It seems the very model of all the catastrophes privileged populations feel await them.”
—Susan Sontag (b. 1933)