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.
Ce cours fait partie de la Spécialisation Modèles graphiques probabilistes
Probabilistic Graphical Models 1: Representation
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À propos de ce cours
4.7
942 notes
Compétences que vous acquerrez
Bayesian NetworkGraphical ModelMarkov Random Field
Programme du cours : ce que vous apprendrez dans ce cours
Semaine
1Introduction 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 vidéos (Total 35 min), 1 quiz
1 exercice pour s'entraîner
Basic Definitions8 min
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 vidéos (Total 190 min), 6 lectures, 4 quiz
15 vidéos
Reasoning Patterns9 min
Flow of Probabilistic Influence14 min
Conditional Independence12 min
Independencies in Bayesian Networks18 min
Naive Bayes9 min
Application - Medical Diagnosis9 min
Knowledge Engineering Example - SAMIAM14 min
Basic Operations 13 min
Moving Data Around 16 min
Computing On Data 13 min
Plotting Data 9 min
Control Statements: for, while, if statements 12 min
Vectorization 13 min
Working on and Submitting Programming Exercises 3 min
6 lectures
Setting Up Your Programming Assignment Environment10 min
Installing Octave/MATLAB on Windows10 min
Installing Octave/MATLAB on Mac OS X (10.10 Yosemite and 10.9 Mavericks)10 min
Installing Octave/MATLAB on Mac OS X (10.8 Mountain Lion and Earlier)10 min
Installing Octave/MATLAB on GNU/Linux10 min
More Octave/MATLAB resources10 min
3 exercices pour s'entraîner
Bayesian Network Fundamentals6 min
Bayesian Network Independencies10 min
Octave/Matlab installation2 min
Semaine
2Template 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 vidéos (Total 66 min), 1 quiz
4 vidéos
Temporal Models - DBNs23 min
Temporal Models - HMMs12 min
Plate Models20 min
1 exercice pour s'entraîner
Template Models20 min
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 vidéos (Total 49 min), 3 quiz
4 vidéos
Tree-Structured CPDs14 min
Independence of Causal Influence13 min
Continuous Variables13 min
2 exercices pour s'entraîner
Structured CPDs8 min
BNs for Genetic Inheritance PA Quiz22 min
Semaine
3Markov 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 vidéos (Total 106 min), 3 quiz
7 vidéos
Pairwise Markov Networks10 min
General Gibbs Distribution15 min
Conditional Random Fields22 min
Independencies in Markov Networks4 min
I-maps and perfect maps20 min
Log-Linear Models22 min
Shared Features in Log-Linear Models8 min
2 exercices pour s'entraîner
Markov Networks8 min
Independencies Revisited6 min
Semaine
4Decision 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 vidéos (Total 61 min), 3 quiz
2 exercices pour s'entraîner
Decision Theory8 min
Decision Making PA Quiz18 min
4.7
217 avis25%
a commencé une nouvelle carrière après avoir terminé ces cours
27%
a bénéficié d'un avantage concret dans sa carrière grâce à ce cours
14%
a obtenu une augmentation de salaire ou une promotion
Meilleurs avis
par ST•Jul 13th 2017
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!!
par CM•Oct 23rd 2017
The course was deep, and well-taught. This is not a spoon-feeding course like some others. The only downside were some "mechanical" problems (e.g. code submission didn't work for me).
Enseignant
Daphne Koller
ProfessorSchool of Engineering
À propos de Université de Stanford
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.
À propos de la Spécialisation Modèles graphiques probabilistes
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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Learning Outcomes: By the end of this course, you will be able to
Apply the basic process of representing a scenario as a Bayesian network or a Markov network
Analyze the independence properties implied by a PGM, and determine whether they are a good match for your distribution
Decide which family of PGMs is more appropriate for your task
Utilize extra structure in the local distribution for a Bayesian network to allow for a more compact representation, including tree-structured CPDs, logistic CPDs, and linear Gaussian CPDs
Represent a Markov network in terms of features, via a log-linear model
Encode temporal models as a Hidden Markov Model (HMM) or as a Dynamic Bayesian Network (DBN)
Encode domains with repeating structure via a plate model
Represent a decision making problem as an influence diagram, and be able to use that model to compute optimal decision strategies and information gathering strategies
Honors track learners will be able to apply these ideas for complex, real-world problems
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