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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 factor graph

The Markov network doesn't give a very clear picture of the Gibbs parameterization of the distribution because we can't conclude whether the factors in it involve the maximal cliques or subgraphs. To overcome this limitation of the Markov network, we require a representation that can show the parameterization explicitly. The factor graph is one such representation.

A factor graph is a bipartite graph, one disjoint set being variable nodes, representing the variables, and the other being factor nodes, representing factors. An edge between a variable node and a factor node denotes that the random variable belongs to the scope of the factor. Thus, a factor graph is parameterized by a set of factors, where each of them is associated with a factor node, whose scope is all sets of all the random variables that it is neighbor to.

Generally, all the variable nodes are represented by a circle and all the factor nodes are represented by a square. Here's an example:

The factor graph

Fig...

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