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 second in a sequence of three. Following the first course, which focused on representation, this course addresses the question of probabilistic inference: how a PGM can be used to answer questions. Even though a PGM generally describes a very high dimensional distribution, its structure is designed so as to allow questions to be answered efficiently. The course presents both exact and approximate algorithms for different types of inference tasks, and discusses where each could best be applied. The (highly recommended) honors track contains two hands-on programming assignments, in which key routines of the most commonly used exact and approximate algorithms are implemented and applied to a real-world problem.
This course is part of the Probabilistic Graphical Models Specialization
Probabilistic Graphical Models 2: Inference
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About this Course
4.6
291 ratings
Skills you will gain
InferenceGibbs SamplingMarkov Chain Monte Carlo (MCMC)Belief Propagation
Syllabus - What you will learn from this course
Week
1Inference Overview
This module provides a high-level overview of the main types of inference tasks typically encountered in graphical models: conditional probability queries, and finding the most likely assignment (MAP inference).
2 videos (Total 25 min)
Variable Elimination
This module presents the simplest algorithm for exact inference in graphical models: variable elimination. We describe the algorithm, and analyze its complexity in terms of properties of the graph structure.
4 videos (Total 56 min), 1 quiz
4 videos
Complexity of Variable Elimination12m
Graph-Based Perspective on Variable Elimination15m
Finding Elimination Orderings11m
1 practice exercise
Variable Elimination18m
Week
2Belief Propagation Algorithms
This module describes an alternative view of exact inference in graphical models: that of message passing between clusters each of which encodes a factor over a subset of variables. This framework provides a basis for a variety of exact and approximate inference algorithms. We focus here on the basic framework and on its instantiation in the exact case of clique tree propagation. An optional lesson describes the loopy belief propagation (LBP) algorithm and its properties.
9 videos (Total 150 min), 3 quizzes
9 videos
Properties of Cluster Graphs15m
Properties of Belief Propagation9m
Clique Tree Algorithm - Correctness18m
Clique Tree Algorithm - Computation16m
Clique Trees and Independence15m
Clique Trees and VE16m
BP In Practice15m
Loopy BP and Message Decoding21m
2 practice exercises
Message Passing in Cluster Graphs10m
Clique Tree Algorithm10m
Week
3MAP Algorithms
This module describes algorithms for finding the most likely assignment for a distribution encoded as a PGM (a task known as MAP inference). We describe message passing algorithms, which are very similar to the algorithms for computing conditional probabilities, except that we need to also consider how to decode the results to construct a single assignment. In an optional module, we describe a few other algorithms that are able to use very different techniques by exploiting the combinatorial optimization nature of the MAP task.
5 videos (Total 74 min), 1 quiz
5 videos
Finding a MAP Assignment3m
Tractable MAP Problems15m
Dual Decomposition - Intuition17m
Dual Decomposition - Algorithm16m
1 practice exercise
MAP Message Passing4m
Week
4Sampling Methods
In this module, we discuss a class of algorithms that uses random sampling to provide approximate answers to conditional probability queries. Most commonly used among these is the class of Markov Chain Monte Carlo (MCMC) algorithms, which includes the simple Gibbs sampling algorithm, as well as a family of methods known as Metropolis-Hastings.
5 videos (Total 100 min), 3 quizzes
5 videos
Markov Chain Monte Carlo14m
Using a Markov Chain15m
Gibbs Sampling19m
Metropolis Hastings Algorithm27m
2 practice exercises
Sampling Methods14m
Sampling Methods PA Quiz8m
Inference in Temporal Models
In this brief lesson, we discuss some of the complexities of applying some of the exact or approximate inference algorithms that we learned earlier in this course to dynamic Bayesian networks.
1 video (Total 20 min), 1 quiz
1 video
1 practice exercise
Inference in Temporal Models6m
4.6
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Top Reviews
By YP•May 29th 2017
I learned pretty much from this course. It answered my quandaries from the representation course, and as well deepened my understanding of PGM.
By JL•Apr 9th 2018
I would have like to complete the honors assignments, unfortunately, I'm not fluent in Matlab. Otherwise, great course!
Instructor
Daphne Koller
ProfessorSchool of Engineering
About 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.
About the Probabilistic Graphical Models Specialization
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.
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?
Is financial aid available?
Learning Outcomes: By the end of this course, you will be able to take a given PGM and
Execute the basic steps of a variable elimination or message passing algorithm
Understand how properties of the graph structure influence the complexity of exact inference, and thereby estimate whether exact inference is likely to be feasible
Go through the basic steps of an MCMC algorithm, both Gibbs sampling and Metropolis Hastings
Understand how properties of the PGM influence the efficacy of sampling methods, and thereby estimate whether MCMC algorithms are likely to be effective
Design Metropolis Hastings proposal distributions that are more likely to give good results
Compute a MAP assignment by exact inference
Honors track learners will be able to implement message passing algorithms and MCMC algorithms, and apply them to a real world problem
More questions? Visit the Learner Help Center.
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