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 part of the Probabilistic Graphical Models Specialization
Probabilistic Graphical Models 2: Inference
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About this Course
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Skills you will gain
InferenceGibbs SamplingMarkov Chain Monte Carlo (MCMC)Belief Propagation
Learner Career Outcomes
50%
started a new career after completing these courses
20%
got a tangible career benefit from this course
20%
got a pay increase or promotion
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Advanced Level
Approx. 24 hours to complete
English
Subtitles: English
Syllabus - What you will learn from this course
25 minutes to complete
Inference 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).
25 minutes to complete
2 videos (Total 25 min)
1 hour to complete
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.
1 hour to complete
4 videos (Total 56 min)
4 videos
Complexity of Variable Elimination12m
Graph-Based Perspective on Variable Elimination15m
Finding Elimination Orderings11m
1 practice exercise
Variable Elimination18m
18 hours to complete
Belief 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.
18 hours to complete
9 videos (Total 150 min)
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
1 hour to complete
MAP 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.
1 hour to complete
5 videos (Total 74 min)
5 videos
Finding a MAP Assignment3m
Tractable MAP Problems15m
Dual Decomposition - Intuition17m
Dual Decomposition - Algorithm16m
1 practice exercise
MAP Message Passing4m
14 hours to complete
Sampling 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.
14 hours to complete
5 videos (Total 100 min)
5 videos
Markov Chain Monte Carlo14m
Using a Markov Chain15m
Gibbs Sampling19m
Metropolis Hastings Algorithm27m
2 practice exercises
Sampling Methods14m
Sampling Methods PA Quiz8m
26 minutes to complete
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.
26 minutes to complete
1 video (Total 20 min)
1 video
1 practice exercise
Inference in Temporal Models6m
Reviews
4.6
TOP REVIEWS FROM PROBABILISTIC GRAPHICAL MODELS 2: INFERENCE
by ATAug 22, 2019
Just like the first course of the specialization, this course is really good. It is well organized and taught in the best way which really helped me to implement similar ideas for my projects.
by ALAug 19, 2019
I have clearly learnt a lot during this course. Even though some things should be updated and maybe completed, I would definitely recommend it to anyone whose interest lies in PGMs.
by LCJul 31, 2018
Very good course. Subject is quiet complex: lack of concrete examples to make sure concepts well understood. Had to review each the Course twice to understand concepts well
by LLMar 11, 2017
Thanks a lot for professor D.K.'s great course for PGM inference part. Really a very good starting point for PGM model and preparation for learning part.
by YPMay 28, 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 JLApr 8, 2018
I would have like to complete the honors assignments, unfortunately, I'm not fluent in Matlab. Otherwise, great course!
by GVNov 27, 2017
great course, though really advanced. would like a bit more examples especially regarding the coding. worth it overally
by EZMar 9, 2018
Very interesting course. However, even after completing it with honors, I feel like I don't understand a lot.
by KDNov 4, 2018
Great introduction.\n\nIt would be great to have more examples included in the lectures and slides.
by AAMar 8, 2020
Great course, except that the programming assignments are in Matlab rather than Python
by ASNov 7, 2017
Great introduction to inference. Requires some extra reading from the textbook.
by SPJun 23, 2017
Had a wonderful and enriching fun filled experience, Thank you Daphne Ma'am
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.