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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

The optimization problem

Let's start with a little recap of exact inference. Assume that we have a factorized distribution in the following form:

The optimization problem

Here, Z is the partition function, The optimization problem are the factors in the network, and The optimization problem is the scope of the factor The optimization problem. In the case of exact inference, we computed The optimization problem and then answered queries over this distribution.

In the case of belief propagation, the end result of running the algorithm was a set of beliefs on the clusters and sepsets. This set of beliefs was able to represent the joint distribution The optimization problem. So, in the case of exact inference, we tried to find a set of calibrated beliefs that was able to represent our joint distribution exactly. For approximate algorithms, we will try to select the set of beliefs from all the sets of beliefs that conform to the cluster tree and are best able to represent our original distribution The optimization problem.

So now the question is, how do we compare the similarity between these two distributions? There are many methods that we can use to compute...

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