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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

Applications

One of the major applications of the HMM is in the field of speech recognition. In this section, we will briefly describe the process of speech recognition.

In speech recognition, our job is to compute the most probable word corresponding to a speech signal or acoustic observation. Our aim is to compute the following:

Here, O corresponds to the acoustic observation and W is the set of all possible words. The likelihood is determined by an acoustic model, and the prior P(W) is determined by a language model.

Fig 7.14 shows the architecture of an HMM-based speech recognition system. There are three major components:

  • Acoustic model

  • Language model

  • Pronunciation dictionary

Fig 7.14: Architecture of an HMM-based speech recognition system

The acoustic model

The basic units of sound represented by the acoustic model are the phonetics. For example, the word "bat" is composed of three phonetics, /b/ /ae/ /t/. About 40 such phonetics are required for English. Each spoken letter W can be decomposed...

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