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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 : 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

Maximum likelihood parameter estimation

As in the case of Bayesian networks, we can also estimate the parameters in the case of Markov networks using maximum likelihood. Let's see in detail how maximum likelihood works in the case of Markov networks.

Likelihood function

Let's take a very simple example of the network, X — Y — Z. We have two potentials, Likelihood function and Likelihood function. We can now define the joint distribution over this network as follows:

Likelihood function

Here, Z is the partition function and is defined as follows:

Likelihood function

Therefore, the log-likelihood equation for a single instance <x, y, z> would be as follows:

Likelihood function

Suppose we have a dataset D containing M samples, we can write the likelihood in the following way:

Likelihood function

Thus, the log-likelihood equation translates to the following formula:

Likelihood function

As we have seen in the case of Bayesian networks, once we have sufficient statistics that summarize the data (the joint count of the variables), we can learn the parameter, Likelihood function. However, with Markov models, the problem is the...

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