Probabilistic graphical models (PGMs) are a rich framework for encoding probability distributions over complex domains: joint (multivariate) distributions over large numbers of random variables that interact with each other. These representations sit at the intersection of statistics and computer science, relying on concepts from probability theory, graph algorithms, machine learning, and more. They are the basis for the state-of-the-art methods in a wide variety of applications, such as medical diagnosis, image understanding, speech recognition, natural language processing, and many, many more. They are also a foundational tool in formulating many machine learning problems.

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## About this Course

### Learner Career Outcomes

## 43%

## 29%

## 17%

#### Shareable Certificate

#### 100% online

#### Course 3 of 3 in the

#### Flexible deadlines

#### Advanced Level

#### Approx. 64 hours to complete

#### English

### Skills you will gain

### Learner Career Outcomes

## 43%

## 29%

## 17%

#### Shareable Certificate

#### 100% online

#### Course 3 of 3 in the

#### Flexible deadlines

#### Advanced Level

#### Approx. 64 hours to complete

#### English

### Offered by

#### Stanford University

The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is an American private research university located in Stanford, California on an 8,180-acre (3,310 ha) campus near Palo Alto, California, United States.

## Syllabus - What you will learn from this course

**16 minutes to complete**

## Learning: Overview

This module presents some of the learning tasks for probabilistic graphical models that we will tackle in this course.

**16 minutes to complete**

**1 video**

**1 hour to complete**

## Review of Machine Learning Concepts from Prof. Andrew Ng's Machine Learning Class (Optional)

This module contains some basic concepts from the general framework of machine learning, taken from Professor Andrew Ng's Stanford class offered on Coursera. Many of these concepts are highly relevant to the problems we'll tackle in this course.

**1 hour to complete**

**6 videos**

**2 hours to complete**

## Parameter Estimation in Bayesian Networks

This module discusses the simples and most basic of the learning problems in probabilistic graphical models: that of parameter estimation in a Bayesian network. We discuss maximum likelihood estimation, and the issues with it. We then discuss Bayesian estimation and how it can ameliorate these problems.

**2 hours to complete**

**5 videos**

**2 practice exercises**

**21 hours to complete**

## Learning Undirected Models

In this module, we discuss the parameter estimation problem for Markov networks - undirected graphical models. This task is considerably more complex, both conceptually and computationally, than parameter estimation for Bayesian networks, due to the issues presented by the global partition function.

**21 hours to complete**

**3 videos**

**1 practice exercise**

**17 hours to complete**

## Learning BN Structure

This module discusses the problem of learning the structure of Bayesian networks. We first discuss how this problem can be formulated as an optimization problem over a space of graph structures, and what are good ways to score different structures so as to trade off fit to data and model complexity. We then talk about how the optimization problem can be solved: exactly in a few cases, approximately in most others.

**17 hours to complete**

**7 videos**

**2 practice exercises**

**22 hours to complete**

## Learning BNs with Incomplete Data

In this module, we discuss the problem of learning models in cases where some of the variables in some of the data cases are not fully observed. We discuss why this situation is considerably more complex than the fully observable case. We then present the Expectation Maximization (EM) algorithm, which is used in a wide variety of problems.

**22 hours to complete**

**5 videos**

**2 practice exercises**

## About the Probabilistic Graphical Models Specialization

## Frequently Asked Questions

When will I have access to the lectures and assignments?

Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

What will I get if I subscribe to this Specialization?

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

What is the refund policy?

If you subscribed, you get a 7-day free trial during which you can cancel at no penalty. After that, we don’t give refunds, but you can cancel your subscription at any time. See our full refund policy.

Is financial aid available?

Yes, Coursera provides financial aid to learners who cannot afford the fee. Apply for it by clicking on the Financial Aid link beneath the "Enroll" button on the left. You'll be prompted to complete an application and will be notified if you are approved. You'll need to complete this step for each course in the Specialization, including the Capstone Project. Learn more.

Learning Outcomes: By the end of this course, you will be able to

Compute the sufficient statistics of a data set that are necessary for learning a PGM from data

Implement both maximum likelihood and Bayesian parameter estimation for Bayesian networks

Implement maximum likelihood and MAP parameter estimation for Markov networks

Formulate a structure learning problem as a combinatorial optimization task over a space of network structure, and evaluate which scoring function is appropriate for a given situation

Utilize PGM inference algorithms in ways that support more effective parameter estimation for PGMs

Implement the Expectation Maximization (EM) algorithm for Bayesian networks

Honors track learners will get hands-on experience in implementing both EM and structure learning for tree-structured networks, and apply them to real-world tasks

More questions? Visit the Learner Help Center.