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Mastering Probabilistic Graphical Models with Python

Mastering Probabilistic Graphical Models with Python

By : Ankur Ankan
3.3 (7)
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Mastering Probabilistic Graphical Models with Python

Mastering Probabilistic Graphical Models with Python

3.3 (7)
By: Ankur Ankan

Overview of this book

Probabilistic Graphical Models is a technique in machine learning that uses the concepts of graph theory to compactly represent and optimally predict values in our data problems. In real world problems, it's often difficult to select the appropriate graphical model as well as the appropriate inference algorithm, which can make a huge difference in computation time and accuracy. Thus, it is crucial to know the working details of these algorithms. 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 to run different inference algorithms on them. There is a complete chapter devoted to the most widely used networks Naive Bayes Model and Hidden Markov Models (HMMs). These models have been thoroughly discussed using real-world examples.
Table of Contents (9 chapters)
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8
Index

Propagation with approximate messages


In the earlier section, we discussed a variant of belief propagation where we relaxed the constraint of having a clique tree, and did belief propagation on a cluster graph. In this section, we will take a different approach. Instead of relaxing on the structure, we will be approximating the messages passed between the clusters. Although this approach can be extended to work with cluster graphs as well, the scope of this book is only limited to clique trees.

Let's consider a simple pairwise Markov model, as shown in Fig 4.9. As discussed in the previous section, a pairwise Markov model is simply a Markov model with the factors associated with each edge , along with the univariate factors corresponding to each random variable . Thus, the following model will have factors such as , , and along with , , , and so on. Let's also assume that each random variable present in this network is binary.

Fig 4.9: Markov model represented by 3 x 3 grid network

A cluster...

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