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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Probabilistic Graphical Models 2: Inference

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Probabilistic Graphical Models 2: Inference

This course is part of Probabilistic Graphical Models Specialization

Instructor: Daphne Koller

26,829 already enrolled

7 modules

Gain insight into a topic and learn the fundamentals.

489 reviews

Advanced level

Designed for those already in the industry

4 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

7 modules

Gain insight into a topic and learn the fundamentals.

489 reviews

Advanced level

Designed for those already in the industry

4 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

Skills you'll gain

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

8 assignments

Taught in English

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This course is part of the Probabilistic Graphical Models Specialization

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There are 7 modules in 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 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.

Module details

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).

What's included

2 videos

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.

What's included

4 videos1 assignment

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.

What's included

9 videos2 assignments1 programming assignment

9 videosTotal 150 minutes

Belief Propagation Algorithm21 minutes
Properties of Cluster Graphs15 minutes
Properties of Belief Propagation10 minutes
Clique Tree Algorithm - Correctness18 minutes
Clique Tree Algorithm - Computation16 minutes
Clique Trees and Independence15 minutes
Clique Trees and VE16 minutes
BP In Practice16 minutes
Loopy BP and Message Decoding22 minutes

2 assignmentsTotal 60 minutes

Message Passing in Cluster Graphs30 minutes
Clique Tree Algorithm30 minutes

1 programming assignmentTotal 900 minutes

Exact Inference900 minutes

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.

What's included

5 videos1 assignment

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.

What's included

5 videos2 assignments1 programming assignment

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.

What's included

1 video1 assignment

This module summarizes some of the topics that we covered in this course and discusses tradeoffs between different algorithms. It also includes the course final exam.