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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

Using a Markov chain


So far, we have been discussing constructing Markov chains. In this section, we will see how to apply these concepts in the case of our graphical models. In the case of probabilistic models, we usually want to compute the posterior probability P(Y|E = e) , and to sample this posterior distribution, we will have to construct a Markov chain whose stationary distribution is P(Y|E = e). So, the states of this Markov chain should be instantiations x of variables and should converge to .

So, for a state in the Markov chain, we define the kernel as follows:

We can see that this transition probability doesn't depend on the current value of of but only on the remaining state . Now, it's really easy to show that the posterior distribution is a stationary distribution of this process.

In graphical models, Gibbs sampling can be very easily implemented in cases where we can compute the transition probability efficiently. We already know the following:

Let denote the assignment...

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