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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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.
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 how to model a real-world situation as a Bayesian network.
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, we use Hidden Markov Models, or, more generally, Dynamic Bayesian Networks. The other is aimed at scenarios that involve multiple similar entities, each of whose properties is governed by a similar model; here, we use Plate Models.
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 representation. Here we describe a number of the ones most commonly used in practice.
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 properties of distributions encoded by these graphs, and their relationship to the graph structure. We compare these independencies to those encoded by a Bayesian network, giving us some insight on which type of model is more suitable for which scenarios.
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 Influence Diagram, and how such models provide insight both into decision making and the value of information gathering.
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来自Probabilistic Graphical Models 1: Representation的热门评论
Prof. Koller did a great job communicating difficult material in an accessible manner. Thanks to her for starting Coursera and offering this advanced course so that we can all learn...Kudos!!
The course was deep, and well-taught. This is not a spoon-feeding course like some others. The only downside were some "mechanical" problems (e.g. code submission didn't work for me).
讲师
Daphne Koller
Professor关于 斯坦福大学
关于 概率图模型 专项课程
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Learning Outcomes: By the end of this course, you will be able to
Apply the basic process of representing a scenario as a Bayesian network or a Markov network
Analyze the independence properties implied by a PGM, and determine whether they are a good match for your distribution
Decide which family of PGMs is more appropriate for your task
Utilize extra structure in the local distribution for a Bayesian network to allow for a more compact representation, including tree-structured CPDs, logistic CPDs, and linear Gaussian CPDs
Represent a Markov network in terms of features, via a log-linear model
Encode temporal models as a Hidden Markov Model (HMM) or as a Dynamic Bayesian Network (DBN)
Encode domains with repeating structure via a plate model
Represent a decision making problem as an influence diagram, and be able to use that model to compute optimal decision strategies and information gathering strategies
Honors track learners will be able to apply these ideas for complex, real-world problems
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