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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

The energy function

In the previous section, we saw that to find the approximate distribution, we need to optimize the relative entropy The energy function, but computing the relative entropy requires us to compute a summation over all possible instantiations of The energy function. To avoid this, we will now try to transform our optimization function in the form of an energy function.

We know the following:

The energy function

Using the product form of The energy function, we have the following:

The energy function

Also, we know that The energy function. Using this in the preceding equation, we get the following:

The energy function
The energy function

Here, The energy function is the energy functional where:

The energy function

The important thing to note here is that Z in the relative entropy term doesn't depend on Q. Hence, minimizing the relative entropy The energy function is equivalent to maximizing the energy function The energy function.

Now, the energy function has two terms. The first one is known as the energy term. The energy term is the summation of the expectations of the logarithm of the factors in The energy function. Therefore, in this term, each factor of The energy function appears separately. Hence, if these factors are small, then...

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