     # Gaussian Mixture Model

## What is a Gaussian Mixture Model?

A Gaussian mixture model is a probabilistic model for representing normally distributed subpopulations among a larger population. It is a type of mixture model used in statistics, that does not require that the observed dataset needs to identify the subpopulation to which an individual observation belongs. The Gaussian mixture model uses two types of values as parameters, the mixture component weights and the component means and variances/covariances.

### Why is this Useful?

Gaussian mixture models allow statistical analysis by something called “unsupervised learning”, where we do not know the correct answers ahead of time and we are trying to estimate/detect patterns in the data. Mixture models allow the analysis of data that is multimodal, meaning there are several different modes to consider. Gaussian mixture models have the ability to form smooth approximations to randomly shaped densities, and it clearly describes the multimodal nature of those densities. Another use is that because numerically sampling from an individual Gaussian distribution is possible, it is fairly easy to obtain a sample from a Gaussian mixture model to create synthetic datasets.

### Practical Uses of a Gaussian Mixture Model

• Biometric Systems

– Gaussian mixture models are commonly used to represent the probability distribution of continuous measurements/features in a biometric system, such as a speaker recognition system.

• System Identification

– The generalized delta rule can be used in systems that need to produce a certain output based on an identified input, such as a surge tank system.