Bayesian Statistics: Mixture Models

This course is part of Bayesian Statistics Specialization

Instructor: Abel Rodriguez

Sponsored by Louisiana Workforce Commission

10,104 already enrolled

5 modules

Gain insight into a topic and learn the fundamentals.

4.5

(58 reviews)

Intermediate level

Recommended experience

21 hours to complete

3 weeks at 7 hours a week

Flexible schedule

Learn at your own pace

5 modules

Gain insight into a topic and learn the fundamentals.

4.5

(58 reviews)

Intermediate level

Recommended experience

21 hours to complete

3 weeks at 7 hours a week

Flexible schedule

Learn at your own pace

What you'll learn

Explain the basic principles behind the algorithm for fitting a mixture model.
Compute the expectation and variance of a mixture distribution.
Use mixture models to solve classification and clustering problems, and to provide density estimates.

Skills you'll gain

Details to know

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Assessments

11 assignments

Taught in English

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There are 5 modules in this course

Bayesian Statistics: Mixture Models introduces you to an important class of statistical models. The course is organized in five modules, each of which contains lecture videos, short quizzes, background reading, discussion prompts, and one or more peer-reviewed assignments. Statistics is best learned by doing it, not just watching a video, so the course is structured to help you learn through application.

Some exercises require the use of R, a freely-available statistical software package. A brief tutorial is provided, but we encourage you to take advantage of the many other resources online for learning R if you are interested. This is an intermediate-level course, and it was designed to be the third in UC Santa Cruz's series on Bayesian statistics, after Herbie Lee's "Bayesian Statistics: From Concept to Data Analysis" and Matthew Heiner's "Bayesian Statistics: Techniques and Models." To succeed in the course, you should have some knowledge of and comfort with calculus-based probability, principles of maximum-likelihood estimation, and Bayesian estimation.

This module defines mixture models, discusses its properties, and develops the likelihood function for a random sample from a mixture model that will be the basis for statistical learning.

What's included

9 videos7 readings7 assignments2 peer reviews1 discussion prompt

9 videosTotal 93 minutes

Welcome to Bayesian Statistics: Mixture Models3 minutesPreview module
Installing and using R5 minutes
Basic definitions25 minutes
Mixtures of Gaussians10 minutes
Zero-inflated mixtures11 minutes
Hierarchical representations7 minutes
Sampling from a mixture model5 minutes
The likelihood function14 minutes
Parameter identifiability10 minutes

7 readingsTotal 70 minutes

An Introduction to R45 minutes
Example of a bimodal mixture of Gaussians3 minutes
Example of a unimodal and skewed mixture of Gaussians3 minutes
Example of a unimodal, symmetric and heavy tailed mixture of Gaussians3 minutes
Example of a zero-inflated negative binomial distribution3 minutes
Example of a zero-inflated log Gaussian distribution3 minutes
Sample code for simulating from a Mixture Model10 minutes

7 assignmentsTotal 38 minutes

Basic definitions6 minutes
Mixtures of Gaussians4 minutes
Zero-inflated distributions4 minutes
The likelihood function0 minutes
Identifiability0 minutes
Definition of Mixture Models20 minutes
Likelihood function for mixture models4 minutes

2 peer reviewsTotal 40 minutes

Likelihood function for mixture models20 minutes
Simulating from a Mixture Model20 minutes

1 discussion promptTotal 15 minutes

When are mixture models helpful?15 minutes

What's included

4 videos2 readings2 peer reviews1 discussion prompt

4 videosTotal 72 minutes

EM for general mixtures24 minutesPreview module
EM for location mixtures of Gaussians22 minutes
EM example 112 minutes
EM example 213 minutes

2 readingsTotal 20 minutes

Sample code for EM example 110 minutes
Sample code for EM example 210 minutes

2 peer reviewsTotal 120 minutes

The EM algorithm for Mixture Models60 minutes
The EM algorithm for zero-inflated mixtures60 minutes

1 discussion promptTotal 10 minutes

Mixtures of log-Gaussians10 minutes

What's included

6 videos2 readings2 peer reviews

6 videosTotal 84 minutes

Markov Chain Monte Carlo algorithms part 112 minutesPreview module
Markov Chain Monte Carlo algorithms, part 213 minutes
MCMC for location mixtures of normals Part 119 minutes
MCMC for location mixtures of normals Part 214 minutes
MCMC Example 111 minutes
MCMC Example 211 minutes

2 readingsTotal 20 minutes

Sample code for MCMC example 110 minutes
Sample code for MCMC example 210 minutes

2 peer reviewsTotal 120 minutes

Markov chain Monte Carlo algorithms for Mixture Models60 minutes
The MCMC algorithm for zero-inflated mixtures60 minutes

What's included

7 videos3 readings3 peer reviews

7 videosTotal 107 minutes

Density estimation using Mixture Models12 minutesPreview module
Density Estimation Example10 minutes
Mixture Models for Clustering23 minutes
Clustering example11 minutes
Mixture Models and naive Bayes classifiers21 minutes
Linear and quadratic discriminant analysis in the context of Mixture Models18 minutes
Classification example10 minutes

3 readingsTotal 30 minutes

Sample code for density estimation problems10 minutes
Sample EM algorithm for clustering problems10 minutes
Sample EM algorithm for classification problems10 minutes

3 peer reviewsTotal 155 minutes

MCMC algorithms and density estimation50 minutes
Classification45 minutes
The EM algorithm and density estimation60 minutes

What's included

7 videos5 readings4 assignments1 peer review1 discussion prompt

7 videosTotal 91 minutes

Numerical stability14 minutesPreview module
Computational issues associated with multimodality11 minutes
Bayesian Information Criteria (BIC)10 minutes
Bayesian Information Criteria Example10 minutes
Estimating the number of components in Bayesian settings9 minutes
Estimating the full partition structure in Bayesian settings18 minutes
Example: Bayesian inference for the partition structure15 minutes

5 readingsTotal 50 minutes

Sample code to illustrate numerical stability issues10 minutes
Sample code to illustrate multimodality issues 110 minutes
Sample code to illustrate multimodality issues 210 minutes
Sample code: Bayesian Information Criteria10 minutes
Sample code for estimating the number of components and the partition structure in Bayesian models10 minutes

4 assignmentsTotal 65 minutes

Bayesian Information Criteria (BIC)30 minutes
Estimating the partition structure in Bayesian models20 minutes
Computational considerations for Mixture Models15 minutes
Estimating the number of components in Bayesian settings0 minutes

1 peer reviewTotal 60 minutes

BIC for zero-inflated mixtures60 minutes

1 discussion promptTotal 30 minutes

Simplifying Binder's expected loss function30 minutes

Instructor

Instructor ratings

4.7 (28 ratings)

Abel Rodriguez

University of California, Santa Cruz

1 Course10,104 learners

Offered by

University of California, Santa Cruz

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Reviewed on Feb 10, 2023

I really enjoyed this course! Plenty of examples on how to use Mixture Models in a Machine Learning context. Thanks to Abel and his team for putting together such an useful course.

Reviewed on Jan 19, 2021

I learned a lot about bayesian mixture model, expectation maximization, and MCMC algorithms and their use case in classification and clustering problems. I highly recommend this course.

Reviewed on Apr 13, 2023

Excellent course to illustrate the model step by step. I like the process of derivation.

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