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  • Book Overview & Buying Mastering Probabilistic Graphical Models with Python
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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

MAP using belief propagation


In the previous section, we discussed the MAP variable elimination algorithm. In the same way that we extended the sum-product variable elimination algorithm for the clique tree and ended up on the belief propagation algorithm, we can perform MAP using the belief propagation. In cases where variable elimination can be computationally intractable, belief propagation has a clear advantage.

The procedure for belief propagation remains the same as discussed in the case of the sum-product. The only thing that changes is the message that is passed between the two clusters and . Earlier, we used to compute messages from to , that is , as follows:

However, now, instead of summing out the variables , we will maximize with respect to them. Thus, the message in the case of MAP belief propagation can be formulated as follows:

When both, the upward pass and the downward pass of the messages are complete, all the adjacent clusters of the tree are said to be max-calibrated....

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