Mixtures gaussianes i algorisme EM

Abstract

[en] In a statistical context, we can define a mixture model as a probabilistic model used to represent the presence of subpopulations within the same population. However, we can also say that a mixture model corresponds to a distribution (formed by a convex linear combination of other distributions) that represents the probability distribution of an observation in a population. Mixture models are used to create statistical inferen- ces, approximations, and predictions about the properties of subpopulations based on observations made about the population studied, without the need to identify the corresponding subpopulation of each observation. In this project, we will study a particular case of mixture models: the Gaussian mixture model (mixture of multivariate Gaussian distributions). The EM algorithm is a method that allows us to estimate the parameters of a statistical model when the data is incomplete or when the model contains unknown variables. In the case of mixture models, the unknown variables are those that tell us which component generated each observation in the sample. In this project, we will study the EM algorithm from different points of view, and we will use it to estimate the parameters of the Gaussian mixture model.