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.

Course 2 of 3 in the Probabilistic Graphical Models Specialization.

### 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).

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.

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.

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.

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.

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.

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.

Graded: Inference Final Exam

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