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Mastering Probabilistic Graphical Models with Python

By : Ankur Ankan
Book Image

Mastering Probabilistic Graphical Models with Python

By: Ankur Ankan

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Mastering Probabilistic Graphical Models with Python
Ankur Ankan
Aug, 2015 | 284 pages
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Table of Contents (14 chapters)
Mastering Probabilistic Graphical Models Using Python
Mastering Probabilistic Graphical Models Using Python
Credits
Credits
About the Authors
About the Authors
About the Reviewers
About the Reviewers
www.PacktPub.com
www.PacktPub.com
Preface
Preface
Free Chapter
1
Bayesian Network Fundamentals
Bayesian Network Fundamentals
Probability theory
Installing tools
Representing independencies using pgmpy
Representing joint probability distributions using pgmpy
Conditional probability distribution
Graph theory
Bayesian models
Relating graphs and distributions
CPD representations
Summary
2
Markov Network Fundamentals
Markov Network Fundamentals
Introducing the Markov network
The factor graph
Independencies in Markov networks
Constructing graphs from distributions
Bayesian and Markov networks
Summary
3
Inference – Asking Questions to Models
Inference – Asking Questions to Models
Inference
Variable elimination
Belief propagation
MAP using variable elimination
Factor maximization
MAP using belief propagation
Finding the most probable assignment
Predictions from the model using pgmpy
A comparison of variable elimination and belief propagation
Summary
4
Approximate Inference
Approximate Inference
The optimization problem
The energy function
Exact inference as an optimization
The propagation-based approximation algorithm
Propagation with approximate messages
Sampling-based approximate methods
Forward sampling
Conditional probability distribution
Likelihood weighting and importance sampling
Importance sampling
Importance sampling in Bayesian networks
Markov chain Monte Carlo methods
Gibbs sampling
The multiple transitioning model
Using a Markov chain
Collapsed particles
Collapsed importance sampling
Summary
5
Model Learning – Parameter Estimation in Bayesian Networks
Model Learning – Parameter Estimation in Bayesian Networks
General ideas in learning
Learning as an optimization
Discriminative versus generative training
Parameter learning
Bayesian parameter estimation
Structure learning in Bayesian networks
The Bayesian score for Bayesian networks
Summary
6
Model Learning – Parameter Estimation in Markov Networks
Model Learning – Parameter Estimation in Markov Networks
Maximum likelihood parameter estimation
Summary
7
Specialized Models
Specialized Models
The Naive Bayes model
Dynamic Bayesian networks
The Hidden Markov model
Applications
Summary
Index
Index

Belief propagation

In the previous section, we saw that the basic operation of the variable elimination algorithm is the manipulation of the factors. First, we create a factor by multiplying existing factors. Then, we eliminate a variable in to generate a new factor , which is then used to create another factor. From a different perspective, we can say that a factor is a data structure, which takes messages generated by the other factor , and generates a message which is used by the other factor .

Clique tree

Before we go into a detailed discussion of the belief propagation algorithm, let's discuss the graphical model that provides the basic framework for it, the clique tree, also known as the junction tree.

The clique tree () is an undirected graph over a set of factors , where each node represents a cluster of random variables and the edges connect the clusters, whose scope has a nonempty intersection. Thus, each edge between a pair of clusters and is associated with a sepset . For...

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