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# Mixture Models in R

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

4 Hours14 Videos47 Exercises

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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!

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1. 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.

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Introduction to model-based clustering
50 xp
Clustering approaches
50 xp
Explore gender data
100 xp
Gaussian distribution
50 xp
Sampling a Gaussian distribution
100 xp
(not so good) Estimations of the mean and sd
100 xp
Gaussian mixture models (GMM)
50 xp
Simulate a mixture of two Gaussian distributions
100 xp
Plot histogram of Gaussian Mixture
100 xp
Mixture of three Gaussian distributions
100 xp
2. 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.

3. 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.

4. 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.

### GroupTraining 2 or more people?

Datasets

Chicago Crimes datasetDigits datasetGender dataset

Collaborators

Victor Medina

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