Probabilistic Graphical Models 1: Representation
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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 first in a sequence of three. It describes the two basic PGM representations: Bayesian Networks, which rely on a directed graph; and Markov networks, which use an undirected graph. The course discusses both the theoretical properties of these representations as well as their use in practice. The (highly recommended) honors track contains several hands-on assignments on how to represent some real-world problems. The course also presents some important extensions beyond the basic PGM representation, which allow more complex models to be encoded compactly.

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  • Week 1 - Introduction and Overview
    This module provides an overall introduction to probabilistic graphical models, and defines a few of the key concepts that will be used later in the course.
  • Week 1 - Bayesian Network (Directed Models)
    In this module, we define the Bayesian network representation and its semantics. We also analyze the relationship between the graph structure and the independence properties of a distribution represented over that graph. Finally, we give some practical tips on...
  • Week 2 - Template Models for Bayesian Networks
    In many cases, we need to model distributions that have a recurring structure. In this module, we describe representations for two such situations. One is temporal scenarios, where we want to model a probabilistic structure that holds constant over time; here,...
  • Week 2 - Structured CPDs for Bayesian Networks
    A table-based representation of a CPD in a Bayesian network has a size that grows exponentially in the number of parents. There are a variety of other form of CPD that exploit some type of structure in the dependency model to allow for a much more compact repr...
  • Week 3 - Markov Networks (Undirected Models)
    In this module, we describe Markov networks (also called Markov random fields): probabilistic graphical models based on an undirected graph representation. We discuss the representation of these models and their semantics. We also analyze the independence prop...
  • Week 4 - Decision Making
    In this module, we discuss the task of decision making under uncertainty. We describe the framework of decision theory, including some aspects of utility functions. We then talk about how decision making scenarios can be encoded as a graphical model called an ...
  • Week 5 - Knowledge Engineering & Summary
    This module provides an overview of graphical model representations and some of the real-world considerations when modeling a scenario as a graphical model. It also includes the course final exam.


Daphne Koller
School of Engineering



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.



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