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

Bayesian estimation for the Bayesian network

Similar to the Bayesian case for the estimation of a single parameter, using the Bayesian framework requires us to specify the joint distribution for all the data instances and unknown parameters.

For the parameters we are trying to estimate, if we decide to have the parameters priori independent (which may not be applicable in all cases), then calculating the posterior becomes easier (which is analogous to likelihood decomposition in MLE). If we have a network comprising two nodes (), then we can calculate the posterior of independently of the posterior over , and the same decomposability can be generalized to larger networks.

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