Probabilistic Graphical Models 2: Inference

About 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.

Created by:  Stanford University

• Taught by:  Daphne Koller, Professor

  School of Engineering

Basic Info Course 2 of 3 in the Probabilistic Graphical Models Specialization Level Advanced Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.6 stars Average User Rating 4.6See what learners said Coursework

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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.

Syllabus


WEEK 1


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 videos expand

1. Video: Overview: Conditional Probability Queries
2. Video: Overview: MAP Inference

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 expand

1. Video: Variable Elimination Algorithm
2. Video: Complexity of Variable Elimination
3. Video: Graph-Based Perspective on Variable Elimination
4. Video: Finding Elimination Orderings

Graded: Variable Elimination

WEEK 2


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 videos expand

1. Video: Belief Propagation Algorithm
2. Video: Properties of Cluster Graphs
3. Video: Properties of Belief Propagation
4. Video: Clique Tree Algorithm - Correctness
5. Video: Clique Tree Algorithm - Computation
6. Video: Clique Trees and Independence
7. Video: Clique Trees and VE
8. Video: BP In Practice
9. Video: Loopy BP and Message Decoding

Graded: Message Passing in Cluster Graphs
Graded: Clique Tree Algorithm
Graded: Exact Inference

WEEK 3


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 videos expand

1. Video: Max Sum Message Passing
2. Video: Finding a MAP Assignment
3. Video: Tractable MAP Problems
4. Video: Dual Decomposition - Intuition
5. Video: Dual Decomposition - Algorithm

Graded: MAP Message Passing

WEEK 4


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 videos expand

1. Video: Simple Sampling
2. Video: Markov Chain Monte Carlo
3. Video: Using a Markov Chain
4. Video: Gibbs Sampling
5. Video: Metropolis Hastings Algorithm

Graded: Sampling Methods
Graded: Sampling Methods
Graded: Sampling Methods PA Quiz

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 expand

1. Video: Inference in Temporal Models

Graded: Inference in Temporal Models

WEEK 5


Inference Summary
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.


1 video expand

1. Video: Inference: Summary

Graded: Inference Final Exam