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Course

Mixture Models in R

IntermediateSkill Level

4.8+

Updated 08/2024

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

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RProbability & Statistics4 hr14 videos47 Exercises3,600 XP5,179Statement of Accomplishment

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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!

Prerequisites

Intermediate R Introduction to the Tidyverse Foundations of Probability in R

1

Introduction to Mixture Models

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 clustering

Clustering approaches

Explore gender data

Gaussian distribution

Sampling a Gaussian distribution

(not so good) Estimations of the mean and sd

Gaussian mixture models (GMM)

Simulate a mixture of two Gaussian distributions

Plot histogram of Gaussian Mixture

Mixture of three Gaussian distributions

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 models

Which probability distribution?

Handwritten digits dataset

Parameters estimation

Estimation given the probabilities

Calculating the probabilities

EM algorithm

Expectation function

Maximization function

Apply the two steps

Plot the estimated clusters

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 Models

Number of clusters

Number of parameters

Univariate Gaussian Mixture Models with flexmix

Univariate case with flexmix

Extracting Parameters for Univariate Case

Visualizing Univariate Gaussian Mixture Model

Compare the results

Bivariate Gaussian Mixture Models

Cross-term from covariance matrix

Parameters in the bivariate case

Bivariate Gaussian Mixture Models with flexmix

Fit the model with cross-terms

Get the components

Create the ellipses

Visualize the clusters

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 Models

Binary images

How many values?

Bernoulli Mixture Models with flexmix

Handwritten digits with `flexmix`

Poisson Mixture Models

Discover the lambda

Sample from Poisson distribution

Poisson Mixture Models with flexmix

Crimes data with `flexmix`

Mixture Models in R

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FAQs

How do mixture models differ from standard clustering techniques like k-means?

Unlike standard clustering, mixture models estimate the probability of each data point belonging to a cluster and allow formal statistical inference about sub-populations using known probability distributions.

Which R package is used to fit mixture models in this course?

The course uses the flexmix package to fit Gaussian and non-Gaussian mixture models, covering both one-dimensional and two-dimensional data.

What real datasets are used in the course?

You will work with a dataset of 10,000 people with weight, height, BMI, and gender data, plus handwritten digit images and crime data from Chicago communities.

Does the course cover the Expectation-Maximization algorithm?

Yes, Chapter 2 teaches the Expectation-Maximization algorithm as the iterative method for estimating mixture model parameters, along with the overall structure of these models.

What types of probability distributions are used beyond Gaussian?

Chapter 4 extends mixture models to non-Gaussian distributions, applying them to handwritten digit classification and crime pattern analysis using the flexmix package.

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