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Mastering Probabilistic Graphical Models with Python

Mastering Probabilistic Graphical Models with Python

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

Mastering Probabilistic Graphical Models with Python

3.3 (7)
By: 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

Exact inference as an optimization


Before considering the approximate inference methods, let's solve the exact inference problem using the concepts that we have so far developed in this chapter. In the previous sections, we saw that maximizing the energy function is equivalent to minimizing the relative entropy between Q and . So now, if we restrict ourselves to calibrated cluster trees, we can further simplify the objective function. Restricting ourselves to calibrated cluster trees allows us to rewrite the energy function in a factored form as a sum of terms, each depending directly on only one of the beliefs in Q. This form also reveals structure in the distribution, and is therefore a much better starting point for further analysis.

Given a cluster tree T with a set of beliefs Q and an assignment , which maps factors in to clusters in T, we define the factored energy function as follows:

Here, is the initial potential assigned to :

Here, represents the expectation on the value given...

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