Probabilistic Graphical Models 1: Representation from Coursera

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.

This course is the first in a sequence of three. It describes the two basic PGM representations: Bayesian Networks, which rely on a directed graph; and Markov networks, which use an undirected graph. The course discusses both the theoretical properties of these representations as well as their use in practice. The (highly recommended) honors track contains several hands-on assignments on how to represent some real-world problems. The course also presents some important extensions beyond the basic PGM representation, which allow more complex models to be encoded compactly.

What's inside

Syllabus

Introduction and Overview

This module provides an overall introduction to probabilistic graphical models, and defines a few of the key concepts that will be used later in the course.

Bayesian Network (Directed Models)

In this module, we define the Bayesian network representation and its semantics. We also analyze the relationship between the graph structure and the independence properties of a distribution represented over that graph. Finally, we give some practical tips on how to model a real-world situation as a Bayesian network.

Template Models for Bayesian Networks

In many cases, we need to model distributions that have a recurring structure. In this module, we describe representations for two such situations. One is temporal scenarios, where we want to model a probabilistic structure that holds constant over time; here, we use Hidden Markov Models, or, more generally, Dynamic Bayesian Networks. The other is aimed at scenarios that involve multiple similar entities, each of whose properties is governed by a similar model; here, we use Plate Models.

Structured CPDs for Bayesian Networks

A table-based representation of a CPD in a Bayesian network has a size that grows exponentially in the number of parents. There are a variety of other form of CPD that exploit some type of structure in the dependency model to allow for a much more compact representation. Here we describe a number of the ones most commonly used in practice.

Markov Networks (Undirected Models)

In this module, we describe Markov networks (also called Markov random fields): probabilistic graphical models based on an undirected graph representation. We discuss the representation of these models and their semantics. We also analyze the independence properties of distributions encoded by these graphs, and their relationship to the graph structure. We compare these independencies to those encoded by a Bayesian network, giving us some insight on which type of model is more suitable for which scenarios.

Decision Making

In this module, we discuss the task of decision making under uncertainty. We describe the framework of decision theory, including some aspects of utility functions. We then talk about how decision making scenarios can be encoded as a graphical model called an Influence Diagram, and how such models provide insight both into decision making and the value of information gathering.

Knowledge Engineering & Summary

This module provides an overview of graphical model representations and some of the real-world considerations when modeling a scenario as a graphical model. It also includes the course final exam.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Examines probabilistic graphical models, which are highly relevant in machine learning

Teaches Bayesian Network and Markov Network representations, which are core models in probabilistic graphical models

Provides hands-on assignments to apply the learned concepts

Offers template models for Bayesian Networks to simplify the modeling of complex problems

Introduces structured CPDs for Bayesian Networks, allowing for more compact representations

Requires prior knowledge of probability theory, graph algorithms, machine learning

Reviews summary

Graphical models: theory & practice

Learners say this course dives into advanced topics in probabilistic graphical models, providing a comprehensive overview. They appreciate the engaging lectures and real-world examples. However, be prepared for difficult programming assignments in Matlab/Octave and limited support from instructors or TAs.

Clear explanations and helpful examples

"The instructor provide clear explanations and useful examples."

"Excellent lecturer who explains clearly pretty complex notions through carefully selected examples."

"She conveys hard stuff in a very lucid manner."

In-depth, comprehensive, and covers advanced topics

"A comprehensive introduction and review of how to represent joint probability distributions as graphs and basic causal reasoning and decision making."

"The course content is really interesting and Daphne Koller is a fabulous presenter."

"Immersing and challenging course. Advises lots of ways for further study in the field."

Challenging but rewarding, especially with optional honors assignments

"This is not an easy course, so beware."

"This course has been retired since old platform discontinued June 2016 . There seems little hope of it appearing on new platform which is a shame . The course paralleled a real Stanford graduate course"

"Wow, it was a hard course. And it is usually true for hard courses, I really learned a lot."

Limited interaction on discussion boards and from TAs/Mentors

"The course content is really interesting and Daphne Koller is a fabulous presenter. Unfortunately, though, you are doing this course on your own - looks like there have been no TAs online for over 3 years, and if you're looking for support or assistance understanding any of the work you may find confusing or difficult then don't expect to get it here."

"This review is for the whole Specialization, not just course 1. The lectures & subject matter are fascinating, but the course itself has some serious limitations:1) Two of the most common example problems the instructor uses are image segmentation & speech recognition, both of which have been completely superseded thanks to neural networks (CNNs for the former, RNNs for the latter)."

Difficult and frustrating, especially in Matlab/Octave

"The programming assignments are infuriating given the large number of bugs."

"This course captures very advanced concepts about probabilistic inference. I found the lectures are more interesting but I wish some explainations were more elaborative, as some concepts are hard to grasp."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Probabilistic Graphical Models 1: Representation with these activities:

Review the text: Probabilistic Graphical Models: Principles and Techniques

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Reviewing this book will provide the background knowledge needed to understand the fundamentals of probabilistic graphical models.

View Probabilistic Graphical Models: Principles and... on Amazon

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Read the introduction and first two chapters of the book.
Summarize the key concepts of Bayesian networks.
Summarize the key concepts of Markov networks.

Watch video tutorials on probabilistic graphical models

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Watching video tutorials can provide students with an additional way to learn the material and reinforce the concepts.

Browse courses on Bayesian Networks

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Find a set of video tutorials on probabilistic graphical models.
Watch the tutorials.
Take notes on the key concepts.

Attend a peer study group to discuss course material

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Peer study groups can provide students with an opportunity to discuss the material with other students and get help with difficult concepts.

Browse courses on Bayesian Networks

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Find a peer study group.
Attend the study group regularly.
Participate in discussions.

Four other activities

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Solve practice problems on Bayesian networks and Markov networks

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Solving practice problems will help students develop a deeper understanding of the concepts and algorithms used in probabilistic graphical models.

Browse courses on Bayesian Networks

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Find a set of practice problems online or in a textbook.
Solve the problems using the techniques learned in the course.
Check your answers against the provided solutions.

Attend a workshop on probabilistic graphical models

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Workshops can provide students with an opportunity to learn from experts in the field and get hands-on experience with probabilistic graphical models.

Browse courses on Bayesian Networks

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Find a workshop on probabilistic graphical models.
Attend the workshop.
Participate in the activities.

Create a graphical model to represent a real-world problem

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Creating a graphical model will help students apply the concepts of probabilistic graphical models to a real-world problem.

Browse courses on Bayesian Networks

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Identify a real-world problem that can be represented as a graphical model.
Choose the appropriate type of graphical model (Bayesian network or Markov network).
Construct the graphical model.
Estimate the parameters of the graphical model.
Use the graphical model to make predictions or inferences about the real-world problem.

Participate in a competition on probabilistic graphical models

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Competitions can provide students with a way to test their skills and knowledge of probabilistic graphical models and to learn from others.

Browse courses on Bayesian Networks

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Find a competition on probabilistic graphical models.
Register for the competition.
Prepare for the competition.
Compete in the competition.

Career center

Learners who complete Probabilistic Graphical Models 1: Representation will develop knowledge and skills that may be useful to these careers:

Machine Learning Engineer

Machine Learning Engineers use their knowledge of algorithms and machine learning techniques such as probabilistic graphical models to solve complex problems, often leveraging large datasets. This course teaches the theoretical properties of these representations as well as their use in practice. Completing this course may help you build a foundation for success as a Machine Learning Engineer.

See salaries and explore the career path for Machine Learning Engineer

Data Scientist

Data Scientists apply their knowledge of statistics and programming to extract insights from data. They may use probabilistic graphical models to identify patterns and relationships in large datasets. This course can help you build a foundation in the use of probabilistic graphical models, a valuable tool for Data Scientists.

See salaries and explore the career path for Data Scientist

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data and make investment decisions. They may use probabilistic graphical models to represent complex financial relationships and make predictions about future market behavior. This course can help you build a foundation in the use of probabilistic graphical models, a valuable tool for Quantitative Analysts.

See salaries and explore the career path for Quantitative Analyst

Risk Analyst

Risk Analysts assess and mitigate risks in various industries, including finance, insurance, and healthcare. They may use probabilistic graphical models to represent complex risk factors and make predictions about future events. This course can help you build a foundation in the use of probabilistic graphical models, a valuable tool for Risk Analysts.

See salaries and explore the career path for Risk Analyst

Software Engineer

Software Engineers design, develop, and test software applications. They may use probabilistic graphical models to create software that can handle uncertainty and make predictions. This course can help you build a foundation in the use of probabilistic graphical models, a valuable tool for Software Engineers.

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Operations Research Analyst

Operations Research Analysts use mathematical and analytical methods to solve complex problems in various industries, including manufacturing, logistics, and healthcare. They may use probabilistic graphical models to represent complex operational relationships and make predictions about future outcomes. This course can help you build a foundation in the use of probabilistic graphical models, a valuable tool for Operations Research Analysts.

See salaries and explore the career path for Operations Research Analyst

Statistician

Statisticians collect, analyze, interpret, and present data. They may use probabilistic graphical models to represent complex statistical relationships and make predictions about future events. This course can help you build a foundation in the use of probabilistic graphical models, a valuable tool for Statisticians.

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Project Manager

Project Managers plan and execute projects to achieve specific goals. They may use probabilistic graphical models to represent complex project dependencies and make predictions about future project outcomes. This course may be useful in helping you build a foundation in the use of probabilistic graphical models, a tool that can be valuable for Project Managers.

See salaries and explore the career path for Project Manager

User Experience Researcher

User Experience Researchers study how users interact with products and services. They may use probabilistic graphical models to represent complex user behavior and make predictions about future user experience. This course may be useful in helping you build a foundation in the use of probabilistic graphical models, a tool that can be valuable for User Experience Researchers.

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Business Analyst

Business Analysts assess business needs and develop solutions to improve efficiency and profitability. They may use probabilistic graphical models to represent complex business processes and make predictions about future outcomes. This course may be useful in helping you build a foundation in the use of probabilistic graphical models, a tool that can be valuable for Business Analysts.

See salaries and explore the career path for Business Analyst

Data Analyst

Data Analysts collect, clean, and analyze data to extract insights and inform decision-making. They may use probabilistic graphical models to represent complex data relationships and make predictions about future outcomes. This course may be useful in helping you build a foundation in the use of probabilistic graphical models, a tool that can be valuable for Data Analysts.

See salaries and explore the career path for Data Analyst

Financial Analyst

Financial Analysts evaluate and make recommendations on investments. They may use probabilistic graphical models to represent complex financial relationships and make predictions about future market behavior. This course may be useful in helping you build a foundation in the use of probabilistic graphical models, a tool that can be valuable for Financial Analysts.

See salaries and explore the career path for Financial Analyst

Product Manager

Product Managers oversee the development and launch of new products. They may use probabilistic graphical models to represent complex product features and make predictions about future product success. This course may be useful in helping you build a foundation in the use of probabilistic graphical models, a tool that can be valuable for Product Managers.

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Risk Manager

Risk Managers identify, assess, and mitigate risks in various organizations. They may use probabilistic graphical models to represent complex risk factors and make predictions about future events. This course may be useful in helping you build a foundation in the use of probabilistic graphical models, a tool that can be valuable for Risk Managers.

See salaries and explore the career path for Risk Manager

Market Researcher

Market Researchers conduct research to understand consumer behavior and market trends. They may use probabilistic graphical models to represent complex consumer preferences and make predictions about future market demand. This course may be useful in helping you build a foundation in the use of probabilistic graphical models, a tool that can be valuable for Market Researchers.

See salaries and explore the career path for Market Researcher