# Mixture distributions

## Mixture models

### Gaussian Mixture Models

#### Mixture models

We have a latent variable which is part of the process

The variable is distributed according to parametric distribution, but parameters are different for differnet latent classes.

There are $$K$$ latent classes, and so $$K$$ sets of parameters.

The population is weighted into the $$K$$ classes.

We have a distribution, but we have different parameters for the distribution for different populations.

For example we could observe the height of men and women, where both are normally distributed but with different parameters.

Where there is a normal distribution, this is a Gaussian mixture model.

If there is more than one variable to observe, this is a multivariate Gaussian mixture model.

#### Gaussian Mixture Models (GMM)

In a Gaussian Mixture Model each non latent variable has a normal distriubtion with a mean and variance. For multiple variables there is a covariance matrix.