Book Image

Building Probabilistic Graphical Models with Python

By : Kiran R Karkera
Book Image

Building Probabilistic Graphical Models with Python

By: Kiran R Karkera

Overview of this book

<p>With the increasing prominence in machine learning and data science applications, probabilistic graphical models are a new tool that machine learning users can use to discover and analyze structures in complex problems. The variety of tools and algorithms under the PGM framework extend to many domains such as natural language processing, speech processing, image processing, and disease diagnosis.</p> <p>You've probably heard of graphical models before, and you're keen to try out new landscapes in the machine learning area. This book gives you enough background information to get started on graphical models, while keeping the math to a minimum.</p>

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Building Probabilistic Graphical Models with Python
Kiran R Karkera
Jun, 2014 | 172 pages
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Table of Contents (15 chapters)
Building Probabilistic Graphical Models with Python
Building Probabilistic Graphical Models with Python
Credits
Credits
About the Author
About the Author
About the Reviewers
About the Reviewers
www.PacktPub.com
www.PacktPub.com
Preface
Preface
Free Chapter
1
Probability
Probability
The theory of probability
Goals of probabilistic inference
Conditional probability
The chain rule
The Bayes rule
Interpretations of probability
Random variables
Marginal distribution
Joint distribution
Independence
Conditional independence
Types of queries
Summary
2
Directed Graphical Models
Directed Graphical Models
Graph terminology
Independence and independent parameters
The Bayes network
Reasoning patterns
D-separation
Factorization and I-maps
The Naive Bayes model
Summary
3
Undirected Graphical Models
Undirected Graphical Models
Pairwise Markov networks
The Gibbs distribution
An induced Markov network
Factorization
Flow of influence
Active trail and separation
Structured prediction
The factorization-independence tango
Summary
4
Structure Learning
Structure Learning
The structure learning landscape
Constraint-based structure learning
Score-based learning
Summary
5
Parameter Learning
Parameter Learning
The likelihood function
Parameter learning example using MLE
MLE for Bayesian networks
Bayesian parameter learning example using MLE
Data fragmentation
Effects of data fragmentation on parameter estimation
Bayesian parameter estimation
Bayesian estimation for the Bayesian network
Example of Bayesian estimation
Summary
6
Exact Inference Using Graphical Models
Exact Inference Using Graphical Models
Complexity of inference
Using the Variable Elimination algorithm
The tree algorithm
Summary
7
Approximate Inference Methods
Approximate Inference Methods
The optimization perspective
Steps in the LBP algorithm
Sampling-based methods
Summary
References
References
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Other references
Index
Index

The Bayes network

A Bayes network is a structure that can be represented as a directed acyclic graph, and the data it contains can be seen from the following two points of view:

  • It allows a compact and modular representation of the joint distribution using the chain rule for Bayes network

  • It allows the conditional independence assumptions between vertices to be observed

We shall explore the two ideas in the job interview example that we have seen so far (which is a Bayesian network, by the way).

The modular structure of the Bayes network is the set of local probability models that represent the nature of the dependence of each variable on its parents (Koller et al 3.2.1.1). One probability distribution each exists for Experience and Grades, and a conditional probability distribution (CPD) each exists for Interview and Offer. A CPD specifies a distribution over a random variable, given all the combinations of assignments to its parents. Thus, the modular representation for a given Bayes network...

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