About this course: 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.

Created by: Stanford University

Taught by: Daphne Koller, Professor
School of Engineering

Basic Info	Course 1 of 3 in the Probabilistic Graphical Models Specialization.
Level	Advanced
Language	English
How To Pass	Pass all graded assignments to complete the course.
User Ratings	4.7 stars Average User Rating 4.7See what learners said

Syllabus

WEEK 1

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.

4 videos

Video: Welcome!
Video: Overview and Motivation
Video: Distributions
Video: Factors

Graded: Basic Definitions

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.

15 videos, 6 readings

Video: Semantics & Factorization
Video: Reasoning Patterns
Video: Flow of Probabilistic Influence
Video: Conditional Independence
Video: Independencies in Bayesian Networks
Video: Naive Bayes
Video: Application - Medical Diagnosis
Video: Knowledge Engineering Example - SAMIAM
Reading: Setting Up Your Programming Assignment Environment
Reading: Installing Octave/MATLAB on Windows
Reading: Installing Octave/MATLAB on Mac OS X (10.10 Yosemite and 10.9 Mavericks)
Reading: Installing Octave/MATLAB on Mac OS X (10.8 Mountain Lion and Earlier)
Reading: Installing Octave/MATLAB on GNU/Linux
Reading: More Octave/MATLAB resources
Video: Basic Operations
Video: Moving Data Around
Video: Computing On Data
Video: Plotting Data
Video: Control Statements: for, while, if statements
Video: Vectorization
Video: Working on and Submitting Programming Exercises

Graded: Bayesian Network Fundamentals

Graded: Bayesian Network Independencies

Graded: Octave/Matlab installation

Graded: Simple BN Knowledge Engineering

WEEK 2

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.

4 videos

Video: Overview of Template Models
Video: Temporal Models - DBNs
Video: Temporal Models - HMMs
Video: Plate Models

Graded: Template 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.

4 videos

Video: Overview: Structured CPDs
Video: Tree-Structured CPDs
Video: Independence of Causal Influence
Video: Continuous Variables

Graded: Structured CPDs

Graded: BNs for Genetic Inheritance

Graded: BNs for Genetic Inheritance PA Quiz

WEEK 3

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.

7 videos

Video: Pairwise Markov Networks
Video: General Gibbs Distribution
Video: Conditional Random Fields
Video: Independencies in Markov Networks
Video: I-maps and perfect maps
Video: Log-Linear Models
Video: Shared Features in Log-Linear Models

Graded: Markov Networks

Graded: Independencies Revisited

Graded: Markov Networks for OCR

WEEK 4

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.

3 videos

Video: Maximum Expected Utility
Video: Utility Functions
Video: Value of Perfect Information

Graded: Decision Theory

Graded: Decision Making

Graded: Decision Making PA Quiz

WEEK 5

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.

1 video

Video: Knowledge Engineering

Graded: Representation Final Exam

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Coursework

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Creators

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.

Pricing

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Ratings and Reviews

Rated 4.7 out of 5 of 469 ratings

Very good and excellent course and assignment

learned a lot. lectures were easy to follow and the textbook was able to more fully explain things when I needed it. looking forward to the next course in the series.

Prof. Koller did a great job communicating difficult material in an accessible manner. Thanks to her for starting Coursera and offering this advanced course so that we can all learn...Kudos!!

very nice intuition from the professor Daphne Koller and "compact" in these lectures that dont exceed 15min each. really glad i did the first one, wish i did also the other two parts, certainly will when i find the time. Just as a comment, i mostly enjoyed the programming assignments. they are very well structured and in a very particular manner, which at the same time is the strong and the weak point of the assingment, since at times i undertsood something else than what the actual implementation was. anyway they were really a challenge, and whoever manages to do them should be glad with his work. Thank you prof. Koller for this course!

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Probabilistic Graphical Models 1: Representation

Probabilistic Graphical Models 1: Representation

Probabilistic Graphical Models 1: Representation