Mastering Probabilistic Graphical Models Using Python

Ankur Ankan, Abinash Panda, Abinash Panda

• Publisher: Packt Publishing
• Year: 2015
• eBook ISBN: 9781784395216
• Edition: 1
• Topic: Computer Science
• Subtopic: Virtualisation
• Index: Computer Science

About This Book

• Gain in-depth knowledge of Probabilistic Graphical Models
• Model time-series problems using Dynamic Bayesian Networks
• A practical guide to help you apply PGMs to real-world problems

Who This Book Is For

If you are a researcher or a machine learning enthusiast, or are working in the data science field and have a basic idea of Bayesian learning or probabilistic graphical models, this book will help you to understand the details of graphical models and use them in your data science problems.

What You Will Learn

• Get to know the basics of probability theory and graph theory
• Work with Markov networks
• Implement Bayesian networks
• Exact inference techniques in graphical models such as the variable elimination algorithm
• Understand approximate inference techniques in graphical models such as message passing algorithms
• Sampling algorithms in graphical models
• Grasp details of Naive Bayes with real-world examples
• Deploy probabilistic graphical models using various libraries in Python
• Gain working details of Hidden Markov models with real-world examples

In Detail

Probabilistic graphical models is a technique in machine learning that uses the concepts of graph theory to concisely represent and optimally predict values in our data problems.

Graphical models gives us techniques to find complex patterns in the data and are widely used in the field of speech recognition, information extraction, image segmentation, and modeling gene regulatory networks.

This book starts with the basics of probability theory and graph theory, then goes on to discuss various models and inference algorithms. All the different types of models are discussed along with code examples to create and modify them, and also run different inference algorithms on them. There is an entire chapter that goes on to cover Naive Bayes model and Hidden Markov models. These models have been thoroughly discussed using real-world examples.

Mastering Probabilistic Graphical Models Using Python

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Table of Contents

Mastering Probabilistic Graphical Models Using Python

Credits

About the Authors

About the Reviewers

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Free access for Packt account holders

Preface

What this book covers

What you need for this book

Who this book is for

Conventions

Reader feedback

Customer support

Downloading the example code

Downloading the color images of this book

Errata

Piracy

Questions

1. Bayesian Network Fundamentals

Probability theory

Random variable

Independence and conditional independence

Installing tools

IPython

pgmpy

Representing independencies using pgmpy

Representing joint probability distributions using pgmpy

Conditional probability distribution

Representing CPDs using pgmpy

Graph theory

Nodes and edges

Walk, paths, and trails

Bayesian models

Representation

Factorization of a distribution over a network

Implementing Bayesian networks using pgmpy

Bayesian model representation

Reasoning pattern in Bayesian networks

D-separation

Direct connection

Indirect connection

Relating graphs and distributions

IMAP

IMAP to factorization

CPD representations

Deterministic CPDs

Context-specific CPDs

Tree CPD

Rule CPD

Summary

2. Markov Network Fundamentals

Introducing the Markov network

Parameterizing a Markov network – factor

Factor operations

Gibbs distributions and Markov networks

The factor graph

Independencies in Markov networks

Constructing graphs from distributions

Bayesian and Markov networks

Converting Bayesian models into Markov models

Converting Markov models into Bayesian models

Chordal graphs

Summary

3. Inference – Asking Questions to Models

Inference

Complexity of inference

Variable elimination

Analysis of variable elimination

Finding elimination ordering

Using the chordal graph property of induced graphs

Minimum fill/size/weight/search

Belief propagation

Clique tree

Constructing a clique tree

Message passing

Clique tree calibration

Message passing with division

Factor division

Querying variables that are not in the same cluster

MAP inference

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

The optimization problem

The energy function

Exact inference as an optimization

The propagation-based approximation algorithm

Cluster graph belief propagation

Constructing cluster graphs

Pairwise Markov networks

Bethe cluster graph

Propaga...

Table of contents

• Mastering Probabilistic Graphical Models Using Python