The Gaussian mixture model
The Gaussian mixture model is the first example of a latent variable model. Latent variables are also called hidden variables and are variables that are present in the model but are never observed.
The notion of using unobserved variables can be surprising at first because we might wonder how to estimate the parameters of the distribution of such a variable. In fact, we might wonder what the real meaning of such a latent variable is.
For example, let's say we observe data represented by a group of random variables. This data tends to group into clusters, aggregating together depending on their underlying meaning. For example, we could observe physiological traits from animals and group those data points by species such as dogs, cats, cows, and so on. If we think in terms of generating models, then we can say that, by choosing a group such as for example pony, we will observe features that are specific to this group and not to another group such as cats. However...
