Mixture models

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Context

In statistics (or machine learning, or other data modeling), distributions are usually about modelling a population.

The ability to model the entire population as a single distribution (gaussian, or whatever distribution may be more applicable to the case) into is a simplification that is both descriptive and has predictive use.

Now consider cases where there may be multiple contributions into the same data.

For a stolen example[1], the price of books might be bimodal: paperbacks around ten bucks, hardcovers around twenty. A model that asks to fitting a single gaussian would not summarize or predict very well. A model that asks to fit two would work measurably better.

A mixture model (sometimes mixture distribution) is a density model consisting of a mixture (weighed sum) of independent variables.

Exactly how abstract the idea is varies, because you could choose

other amounts of groups (potentially infinite, but in practice often a relatively small number),

the distribution used for each part (often a gaussian, in which case we're talking about a GMM)

other types of data (not just real-numbered),

more-dimensional data,

more complex models.(verify)

So potentially quite fancy, though in practice (an in examples) usually about modeling a small amount of distrinct contributions, and often with an amount that we have a good reason to choose.

Mixture models

See also

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