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Building Probabilistic Graphical Models with Python.pdf

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    Cover
    Copyright
    Credits
    About the Author
    About the Reviewers
    www.PacktPub.com
    Table of Contents
    Preface
    Chapter 1: 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
    Probability queries
    MAP queries
    Summary
    Chapter 2: Directed Graphical Models
    Graph terminology
    Python digression
    Independence and independent parameters
    The Bayes network
    The chain rule
    Reasoning patterns
    Causal reasoning
    Evidential reasoning
    Inter-causal reasoning
    D-separation
    The D-separation example
    Blocking and unblocking a V-structure
    Factorization and I-maps
    The Naive Bayes model
    The Naïve Bayes example
    Summary
    Chapter 3: Undirected Graphical Models
    Pairwise Markov networks
    The Gibbs distribution
    An induced Markov network
    Factorization
    Flow of influence
    Active trail and separation
    Structured prediction
    Problem of correlated features
    The CRF representation
    The CRF example
    The factorization-independence tango
    Summary
    Chapter 4: Structure Learning
    The structure learning landscape
    Constraint-based structure learning
    Part I
    Part II
    Part III
    Summary of constraint-based approaches
    Score-based learning
    The likelihood score
    The Bayesian information criterion score
    The Bayesian score
    Summary of score-based learning
    Summary
    Chapter 5: Parameter Learning
    The likelihood function
    Parameter learning example using MLE
    MLE for Bayesian networks
    Bayesian parameter learning example using MLE
    Data fragmentation
    Effect of data fragmentation on parameter estimation
    Bayesian parameter estimation
    An example of Bayesian methods for parameter learning
    Bayesian estimation for the Bayesian network
    Example of Bayesian estimation
    Summary
    Chapter 6: Exact Inference Using Graphical Models
    Complexity of inference
    Real-world issues
    Using the Variable Elimination algorithm
    Marginalizing factors that are not relevant
    Factor reduction to filter on evidence
    Shortcomings of the brute-force approach
    Using the Variable Elimination approach
    Complexity of Variable Elimination
    Graph perspective
    Learning the induced width from the graph structure
    The tree algorithm
    The four stages of the junction tree algorithm
    Using the junction tree algorithm for inference
    Stage 1.1 – moralization
    Stage 1.2 – triangulation
    Stage 1.3 – building the join tree
    Stage 2 – initializing potentials
    Stage 3 – message passing
    Summary
    Chapter 7: Approximate Inference Methods
    The optimization perspective
    Belief propagation on general graphs
    Creating a cluster graph to run LBP
    Message passing in LBP
    Steps in the LBP algorithm
    Improving the convergence of LBP
    Applying LBP to segment an image
    Understanding energy-based models
    Visualizing unary and pairwise factors on a 3 x 3 grid
    Creating the model for image segmentation
    Applications of LBP
    Sampling-based methods
    Forward sampling
    The accept-reject sampling method
    The Markov Chain Monte Carlo sampling process
    The Markov property
    The Markov chain
    Reaching a steady state
    Sampling using a Markov chain
    Gibbs sampling
    Steps in the Gibbs sampling procedure
    An example of Gibbs sampling
    Summary
    Appendix: References
    Index
    Building Probabilistic Graphical Models with Python Solve machine learning problems using probabilistic graphical models implemented in Python with real-world applications Kiran R Karkera BIRMINGHAM - MUMBAI
    Building Probabilistic Graphical Models with Python Copyright © 2014 Packt Publishing All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior written permission of the publisher, except in the case of brief quotations embedded in critical articles or reviews. Every effort has been made in the preparation of this book to ensure the accuracy of the information presented. However, the information contained in this book is sold without warranty, either express or implied. Neither the author, nor Packt Publishing, and its dealers and distributors will be held liable for any damages caused or alleged to be caused directly or indirectly by this book. Packt Publishing has endeavored to provide trademark information about all of the companies and products mentioned in this book by the appropriate use of capitals. However, Packt Publishing cannot guarantee the accuracy of this information. First published: June 2014 Production reference: 1190614 Published by Packt Publishing Ltd. Livery Place 35 Livery Street Birmingham B3 2PB, UK. ISBN 978-1-78328-900-4 www.packtpub.com Cover image by Manju Mohanadas (manju.mohanadas@gmail.com) [ FM-2 ]
    Credits Project Coordinator Melita Lobo Proofreaders Maria Gould Joanna McMahon Indexers Mariammal Chettiyar Hemangini Bari Graphics Disha Haria Yuvraj Mannari Abhinash Sahu Production Coordinator Alwin Roy Cover Work Alwin Roy Author Kiran R Karkera Reviewers Mohit Goenka Shangpu Jiang Jing (Dave) Tian Xiao Xiao Commissioning Editor Kartikey Pandey Acquisition Editor Nikhil Chinnari Content Development Editor Madhuja Chaudhari Technical Editor Krishnaveni Haridas Copy Editors Alisha Aranha Roshni Banerjee Mradula Hegde [ FM-3 ]
    About the Author Kiran R Karkera is a telecom engineer with a keen interest in machine learning. He has been programming professionally in Python, Java, and Clojure for more than 10 years. In his free time, he can be found attempting machine learning competitions at Kaggle and playing the flute. I would like to thank the maintainers of Libpgm and OpenGM libraries, Charles Cabot and Thorsten Beier, for their help with the code reviews. [ FM-4 ]
    About the Reviewers Mohit Goenka graduated from the University of Southern California (USC) with a Master's degree in Computer Science. His thesis focused on game theory and human behavior concepts as applied in real-world security games. He also received an award for academic excellence from the Office of International Services at the University of Southern California. He has showcased his presence in various realms of computers including artificial intelligence, machine learning, path planning, multiagent systems, neural networks, computer vision, computer networks, and operating systems. During his tenure as a student, Mohit won multiple competitions cracking codes and presented his work on Detection of Untouched UFOs to a wide range of audience. Not only is he a software developer by profession, but coding is also his hobby. He spends most of his free time learning about new technology and grooming his skills. What adds a feather to Mohit's cap is his poetic skills. Some of his works are part of the University of Southern California libraries archived under the cover of the Lewis Carroll Collection. In addition to this, he has made significant contributions by volunteering to serve the community. Shangpu Jiang is doing his PhD in Computer Science at the University of Oregon. He is interested in machine learning and data mining and has been working in this area for more than six years. He received his Bachelor's and Master's degrees from China. [ FM-5 ]
    Jing (Dave) Tian is now a graduate researcher and is doing his PhD in Computer Science at the University of Oregon. He is a member of the OSIRIS lab. His research direction involves system security, embedded system security, trusted computing, and static analysis for security and virtualization. He is interested in Linux kernel hacking and compilers. He also spent a year on AI and machine learning direction and taught the classes Intro to Problem Solving using Python and Operating Systems in the Computer Science department. Before that, he worked as a software developer in the Linux Control Platform (LCP) group at the Alcatel-Lucent (former Lucent Technologies) R&D department for around four years. He got his Bachelor's and Master's degrees from EE in China. Thanks to the author of this book who has done a good job for both Python and PGM; thanks to the editors of this book, who have made this book perfect and given me the opportunity to review such a nice book. Xiao Xiao is a PhD student studying Computer Science at the University of Oregon. Her research interests lie in machine learning, especially probabilistic graphical models. Her previous project was to compare two inference algorithms' performance on a graphical model (relational dependency network). [ FM-6 ]
    www.PacktPub.com Support files, eBooks, discount offers and more You might want to visit www.PacktPub.com for support files and downloads related to your book. Did you know that Packt offers eBook versions of every book published, with PDF and ePub files available? You can upgrade to the eBook version at www.PacktPub. com and as a print book customer, you are entitled to a discount on the eBook copy. Get in touch with us at service@packtpub.com for more details. At www.PacktPub.com, you can also read a collection of free technical articles, sign up for a range of free newsletters and receive exclusive discounts and offers on Packt books and eBooks. TM http://PacktLib.PacktPub.com Do you need instant solutions to your IT questions? PacktLib is Packt's online digital book library. Here, you can access, read and search across Packt's entire library of books. Why Subscribe? • Fully searchable across every book published by Packt • Copy and paste, print and bookmark content • On demand and accessible via web browser Free Access for Packt account holders If you have an account with Packt at www.PacktPub.com, you can use this to access PacktLib today and view nine entirely free books. Simply use your login credentials for immediate access. [ FM-7 ]
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