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.
Ce cours fait partie de la Spécialisation Modèles graphiques probabilistes
Probabilistic Graphical Models 2: Inference
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À propos de ce cours
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Compétences que vous acquerrez
InferenceGibbs SamplingMarkov Chain Monte Carlo (MCMC)Belief Propagation
Programme du cours : ce que vous apprendrez dans ce cours
Semaine
125 minutes pour terminer
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).
2 vidéos (Total 25 min)
1 heure pour terminer
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 vidéos (Total 56 min), 1 quiz
4 vidéos
Complexity of Variable Elimination12 min
Graph-Based Perspective on Variable Elimination15 min
Finding Elimination Orderings11 min
1 exercice pour s'entraîner
Variable Elimination18 min
Semaine
218 heures pour terminer
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.
9 vidéos (Total 150 min), 3 quiz
9 vidéos
Properties of Cluster Graphs15 min
Properties of Belief Propagation9 min
Clique Tree Algorithm - Correctness18 min
Clique Tree Algorithm - Computation16 min
Clique Trees and Independence15 min
Clique Trees and VE16 min
BP In Practice15 min
Loopy BP and Message Decoding21 min
2 exercices pour s'entraîner
Message Passing in Cluster Graphs10 min
Clique Tree Algorithm10 min
Semaine
31 heure pour terminer
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.
5 vidéos (Total 74 min), 1 quiz
5 vidéos
Max Sum Message Passing20 min
Finding a MAP Assignment3 min
Tractable MAP Problems15 min
Dual Decomposition - Intuition17 min
Dual Decomposition - Algorithm16 min
1 exercice pour s'entraîner
MAP Message Passing4 min
Semaine
414 heures pour terminer
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.
5 vidéos (Total 100 min), 3 quiz
5 vidéos
Simple Sampling23 min
Markov Chain Monte Carlo14 min
Using a Markov Chain15 min
Gibbs Sampling19 min
Metropolis Hastings Algorithm27 min
2 exercices pour s'entraîner
Sampling Methods14 min
Sampling Methods PA Quiz8 min
26 minutes pour terminer
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 vidéo (Total 20 min), 1 quiz
1 vidéo
1 exercice pour s'entraîner
Inference in Temporal Models6 min
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Meilleurs avis
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.
I learned pretty much from this course. It answered my quandaries from the representation course, and as well deepened my understanding of PGM.
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 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
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