# Mixture Models in R

Learn mixture models: a convenient and formal statistical framework for probabilistic clustering and classification.

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## Course Description

Mixture modeling is a way of representing populations when we are interested in their heterogeneity. Mixture models use familiar probability distributions (e.g. Gaussian, Poisson, Binomial) to provide a convenient yet formal statistical framework for clustering and classification. Unlike standard clustering approaches, we can estimate the probability of belonging to a cluster and make inference about the sub-populations. For example, in the context of marketing, you may want to cluster different customer groups and find their respective probabilities of purchasing specific products to better target them with custom promotions. When applying natural language processing to a large set of documents, you may want to cluster documents into different topics and understand how important each topic is across each document. In this course, you will learn what Mixture Models are, how they are estimated, and when it is appropriate to apply them!

- 1
### Introduction to Mixture Models

**Free**In this chapter, you will be introduced to fundamental concepts in model-based clustering and how this approach differs from other clustering techniques. You will learn the generating process of Gaussian Mixture Models as well as how to visualize the clusters.

Introduction to model-based clustering50 xpClustering approaches50 xpExplore gender data100 xpGaussian distribution50 xpSampling a Gaussian distribution100 xp(not so good) Estimations of the mean and sd100 xpGaussian mixture models (GMM)50 xpSimulate a mixture of two Gaussian distributions100 xpPlot histogram of Gaussian Mixture100 xpMixture of three Gaussian distributions100 xp - 2
### Structure of Mixture Models and Parameters Estimation

In this chapter, you will be introduced to the main structure of Mixture Models, how to address different data with this approach and how to estimate the parameters involved. To accomplish the estimation, you will learn an iterative method called Expectation-Maximization algorithm.

Structure of mixture models50 xpWhich probability distribution?50 xpHandwritten digits dataset100 xpParameters estimation50 xpEstimation given the probabilities100 xpCalculating the probabilities100 xpEM algorithm50 xpExpectation function100 xpMaximization function100 xpApply the two steps100 xpPlot the estimated clusters100 xp - 3
### Mixture of Gaussians with `flexmix`

This chapter shows how to fit Gaussian Mixture Models in 1 and 2 dimensions with `flexmix` package. The data used is formed by 10.000 observations of people with their weight, height, body mass index and informed gender.

Univariate Gaussian Mixture Models50 xpNumber of clusters50 xpNumber of parameters50 xpUnivariate Gaussian Mixture Models with flexmix50 xpUnivariate case with flexmix100 xpExtracting Parameters for Univariate Case100 xpVisualizing Univariate Gaussian Mixture Model100 xpCompare the results100 xpBivariate Gaussian Mixture Models50 xpCross-term from covariance matrix50 xpParameters in the bivariate case50 xpBivariate Gaussian Mixture Models with flexmix50 xpFit the model with cross-terms100 xpGet the components100 xpCreate the ellipses100 xpVisualize the clusters100 xp - 4
### Mixture Models Beyond Gaussians

In this module, you will learn how Mixture Models extends to consider probability distributions different from the Gaussian and how these models are fitted with `flexmix`. The datasets used are handwritten digits images and the number of crimes in Chicago city. For the first dataset you will find clusters that summarize the handwritten digits and for the second dataset, you will find clusters of communities where is more or less dangerous to live in.

Bernoulli Mixture Models50 xpBinary images100 xpHow many values?50 xpBernoulli Mixture Models with flexmix50 xpHandwritten digits with `flexmix`100 xpPoisson Mixture Models50 xpDiscover the lambda50 xpSample from Poisson distribution100 xpPoisson Mixture Models with flexmix50 xpCrimes data with `flexmix`100 xp

#### Victor Medina

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